Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: a numerical simulation study

Numerical assessments of geometry, proximity and multi-electrode effects on electroporation in mitochondria and the endoplasmic reticulum to nanosecond electric pulses

Most simulations of electric field driven bioeffects have considered spherical cellular geometries or probed symmetrical structures for simplicity. This work assesses cellular transmembrane potential build-up and electroporation in a Jurkat cell that includes the endoplasmic reticulum (ER) and mitochondria, both of which have complex shapes, in response to external nanosecond electric pulses. The simulations are based on a time-domain nodal analysis that incorporates membrane poration utilizing the Smoluchowski model with angular-dependent changes in membrane conductivity. Consistent with prior experimental reports, the simulations show that the ER requires the largest electric field for electroporation, while the inner mitochondrial membrane (IMM) is the easiest membrane to porate. Our results suggest that the experimentally observed increase in intracellular calcium could be due to a calcium induced calcium release (CICR) process that is initiated by outer cell membrane breakdown. Repeated pulsing and/or using multiple electrodes are shown to create a stronger poration. The role of mutual coupling, screening, and proximity effects in bringing about electric field modifications is also probed. Finally, while including greater geometric details might refine predictions, the qualitative trends are expected to remain.

Process Analysis and Parameter Selection of Cardiomyocyte Electroporation Based on the Finite Element Method

PURPOSE

Pulsed-field ablation (PFA) has attracted attention for the treatment of atrial fibrillation. This study aimed to further explore the relationship between the transmembrane voltage, pore radius and the intensity and duration of pulsed electric fields, which are closely related to the formation of irreversible electroporation. The different mechanisms of microsecond and nanosecond pulses acting on cardiomyocyte cellular and nuclear membranes were studied.

METHODS

A 3-D cardiomyocyte model with a nucleus was constructed to simulate the process of electroporation in cells under an electric field. Cell membrane electroporation was used to simulate the effect of different pulse parameters on the process of electroporation.

RESULTS

Under a single pulse with a field strength of 1 kV/cm and width of 100 μs, the transmembrane potential (TMP) of the cell membrane reached 1.33 V, and the pore density and conductivity increased rapidly. The maximum pore radius of the cell membrane was 43.4 nm, and the electroporation area accounted for 4.6% of the total cell membrane area. The number of pores was positively correlated with the electric field intensity when the cell was exposed to electric fields of 0.5 to 6 kV/cm. Under a nanosecond pulse, the TMP of the nuclear and cell membranes exceeded 1 V after exposure to electric fields with strengths of 4 and 5 kV/cm, respectively.

CONCLUSION

This study simulated the electroporation process of cardiomyocyte, and provides a basis for the selection of parameters for the application of PFA for application toward arrhythmias.

Molecular dynamics insights on temperature and pressure effects on electroporation

Electroporation is a cell-level phenomenon caused by an ionic imbalance in the membrane, being of great relevance in various fields of knowledge. A dependence of the pore formation kinetics on the environmental conditions (temperature and pressure) of the cell membrane has already been reported, but further clarification regarding how these variables affect the pore formation/resealing dynamics and the transport of molecules through the membrane is still lacking. The objective of the present study was to investigate the temperature (288-348 K) and pressure (1-5000 atm) effects on the electroporation kinetics using coarse-grained molecular dynamics simulations. Results shown that the time for pore formation and resealing increased with pressure and decreased with temperature, whereas the maximum pore radius increased with temperature and decreased with pressure. This behavior influenced the ion migration through the bilayer, and the higher ionic mobility was obtained in the 288 K/1000 atm simulations, i.e., a combination of low temperature and (not excessively) high pressure. These results were used to discuss some experimental observations regarding the extraction of intracellular compounds applying this technique. This study contributes to a better understanding of electroporation under different thermodynamic conditions and to an optimal selection of processing parameters in practical applications which exploit this phenomenon.

Cell death due to electroporation - A review

Exposure of cells to high voltage electric pulses increases transiently membrane permeability through membrane electroporation. Electroporation can be reversible and is used in gene transfer and enhanced drug delivery but can also lead to cell death. Electroporation resulting in cell death (termed as irreversible electroporation) has been successfully used as a new non-thermal ablation method of soft tissue such as tumours or arrhythmogenic heart tissue. Even though the mechanisms of cell death can influence the outcome of electroporation-based treatments due to use of different electric pulse parameters and conditions, these are not elucidated yet. We review the mechanisms of cell death after electroporation reported in literature, cell injuries that may lead to cell death after electroporation and membrane repair mechanisms involved. The knowledge of membrane repair and cell death mechanisms after cell exposure to electric pulses, targets of electric field in cells need to be identified to optimize existing and develop of new electroporation-based techniques used in medicine, biotechnology, and food technology.

Continuum analysis to assess field enhancements for tailoring electroporation driven by monopolar or bipolar pulsing based on nonuniformly distributed nanoparticles

Recent reports indicate that nanoparticle (NP) clusters near cell membranes could enhance local electric fields, leading to heightened electroporation. This aspect is quantitatively analyzed through numerical simulations whereby time dependent transmembrane potentials are first obtained on the basis of a distributed circuit mode, and the results then used to calculate pore distributions from continuum Smoluchowski theory. For completeness, both monopolar and bipolar nanosecond-range pulse responses are presented and discussed. Our results show strong increases in TMP with the presence of multiple NP clusters and demonstrate that enhanced poration could be possible even over sites far away from the poles at the short pulsing regime. Furthermore, our results demonstrate that nonuniform distributions would work to enable poration at regions far away from the poles. The NP clusters could thus act as distributed electrodes. Our results were roughly in line with recent experimental observations.

High Throughput and Highly Controllable Methods for In Vitro Intracellular Delivery

In vitro and ex vivo intracellular delivery methods hold the key for releasing the full potential of tissue engineering, drug development, and many other applications. In recent years, there has been significant progress in the design and implementation of intracellular delivery systems capable of delivery at the same scale as viral transfection and bulk electroporation but offering fewer adverse outcomes. This review strives to examine a variety of methods for in vitro and ex vivo intracellular delivery such as flow-through microfluidics, engineered substrates, and automated probe-based systems from the perspective of throughput and control. Special attention is paid to a particularly promising method of electroporation using micro/nanochannel based porous substrates, which expose small patches of cell membrane to permeabilizing electric field. Porous substrate electroporation parameters discussed include system design, cells and cargos used, transfection efficiency and cell viability, and the electric field and its effects on molecular transport. The review concludes with discussion of potential new innovations which can arise from specific aspects of porous substrate-based electroporation platforms and high throughput, high control methods in general.

Soft Electroporation Through 3D Hollow Nanoelectrodes

Generally, electroporation of in vitro cells is performed under very high electric fields to overcome the physical barrier of plasma membrane. Since traditional electroporation techniques make use of very high voltages, which is critical to cell viability, this study presents a microfluidic platform able to perform cell membrane electroporation with the application of low voltages (1.5-2 V). The platform is manufactured based on the milling by mean of focused ionic beam, which offers an established approach to fabricate ordered arrays of 3D gold hollow nanoelectrodes protruding from an insulating substrate. The novelty of this fabrication relies on the fact that the nanoelectrodes used for electroporation are simultaneously metallic, hollow and communicate through its nanochannels with an isolated microfluidic chamber beneath the device. Adherent cultured cells on the nanoelectrodes can be electroporated in this platform, and molecules can be selectively delivered only inside the porated cells.

Combined Numerical and Experimental Investigation of Localized Electroporation-Based Cell Transfection and Sampling

Localized electroporation has evolved as an effective technology for the delivery of foreign molecules into cells while preserving their viability. Consequently, this technique has potential applications in sampling the contents of live cells and the temporal assessment of cellular states at the single-cell level. Although there have been numerous experimental reports on localized electroporation-based delivery, a lack of a mechanistic understanding of the process hinders its implementation in sampling. In this work, we develop a multiphysics model that predicts the transport of molecules into and out of the cell during localized electroporation. Based on the model predictions, we optimize experimental parameters such as buffer conditions, electric field strength, cell confluency, and density of nanochannels in the substrate for successful delivery and sampling via localized electroporation. We also identify that cell membrane tension plays a crucial role in enhancing both the amount and the uniformity of molecular transport, particularly for macromolecules. We qualitatively validate the model predictions on a localized electroporation platform by delivering large molecules (bovine serum albumin and mCherry-encoding plasmid) and by sampling an exogeneous protein (tdTomato) in an engineered cell line.

Anistropically varying conductivity in irreversible electroporation simulations

Background

One recent area of cancer research is irreversible electroporation (IRE). Irreversible electroporation is a minimally invasive procedure where needle electrodes are inserted into the body to ablate tumor cells with electricity. The aim of this paper is to propose a mathematical model that incorporates a tissue’s conductivity increasing more in the direction of the electrical field as this has been shown to occur in experiments.

Method

It was necessary to mathematically derive a valid form of the conductivity tensor such that it is dependent on the electrical field direction and can be easily implemented into numerical software. The derivation of a conductivity tensor that can take arbitrary functions for the conductivity in the directions tangent and normal to the electrical field is the main contribution of this paper. Numerical simulations were performed for isotropic-varying and anisotropic-varying conductivities to evaluate the importance of including the electrical field’s direction in the formulation for conductivity.

Results

By starting from previously published experimental results, this paper derived a general formulation for an anistropic-varying tensor for implementation into irreversible electroporation modeling software. The anistropic-varying tensor formulation allows the conductivity to take into consideration both electrical field direction and magnitude, as opposed to previous published works that only took into account electrical field magnitude.

The anisotropic formulation predicts roughly a five percent decrease in ablation size for the monopolar simulation and approximately a ten percent decrease in ablation size for the bipolar simulations. This is a positive result as previously reported results found the isotropic formulation to overpredict ablation size for both monopolar and bipolar simulations. Furthermore, it was also reported that the isotropic formulation overpredicts the ablation size more for the bipolar case than the monopolar case. Thus, our results are following the experimental trend by having a larger percentage change in volume for the bipolar case than the monopolar case.

Conclusions

The predicted volume of ablated cells decreased, and could be a possible explanation for the slight over-prediction seen by isotropic-varying formulations.

Soft electroporation for delivering molecules into tightly adherent mammalian cells through 3D hollow nanoelectrodes

Electroporation of in-vitro cultured cells is widely used in biological and medical areas to deliver molecules of interest inside cells. Since very high electric fields are required to electroporate the plasma membrane, depending on the geometry of the electrodes the required voltages can be very high and often critical to cell viability. Furthermore, in traditional electroporation configuration based on planar electrodes there is no a priori certain feedback about which cell has been targeted and delivered and the addition of fluorophores may be needed to gain this information. In this study we present a nanofabricated platform able to perform intracellular delivery of membrane-impermeable molecules by opening transient nanopores into the lipid membrane of adherent cells with high spatial precision and with the application of low voltages (1.5–2 V). This result is obtained by exploiting the tight seal that the cells present with 3D fluidic hollow gold-coated nanostructures that act as nanochannels and nanoelectrodes at the same time. The final soft-electroporation platform provides an accessible approach for controlled and selective drug delivery on ordered arrangements of cells.

Technical difficulties and solutions of direct transesterification process of microbial oil for biodiesel synthesis

Microbial oils are considered as alternative to vegetable oils or animal fats as biodiesel feedstock. Microalgae and oleaginous yeast are the main candidates of microbial oil producers' community. However, biodiesel synthesis from these sources is associated with high cost and process complexity. The traditional transesterification method includes several steps such as biomass drying, cell disruption, oil extraction and solvent recovery. Therefore, direct transesterification or in situ transesterification, which combines all the steps in a single reactor, has been suggested to make the process cost effective. Nevertheless, the process is not applicable for large-scale biodiesel production having some difficulties such as high water content of biomass that makes the reaction rate slower and hurdles of cell disruption makes the efficiency of oil extraction lower. Additionally, it requires high heating energy in the solvent extraction and recovery stage. To resolve these difficulties, this review suggests the application of antimicrobial peptides and high electric fields to foster the microbial cell wall disruption.

A microfluidic biochip for complete blood cell counts at the point-of-care

Complete blood cell counts (CBCs) are one of the most commonly ordered and informative blood tests in hospitals. The results from a CBC, which typically include white blood cell (WBC) counts with differentials, red blood cell (RBC) counts, platelet counts and hemoglobin measurements, can have implications for the diagnosis and screening of hundreds of diseases and treatments. Bulky and expensive hematology analyzers are currently used as a gold standard for acquiring CBCs. For nearly all CBCs performed today, the patient must travel to either a hospital with a large laboratory or to a centralized lab testing facility. There is a tremendous need for an automated, portable point-of-care blood cell counter that could yield results in a matter of minutes from a drop of blood without any trained professionals to operate the instrument. We have developed microfluidic biochips capable of a partial CBC using only a drop of whole blood. Total leukocyte and their 3-part differential count are obtained from 10 μL of blood after on-chip lysing of the RBCs and counting of the leukocytes electrically using microfabricated platinum electrodes. For RBCs and platelets, 1 μL of whole blood is diluted with PBS on-chip and the cells are counted electrically. The total time for measurement is under 20 minutes. We demonstrate a high correlation of blood cell counts compared to results acquired with a commercial hematology analyzer. This technology could potentially have tremendous applications in hospitals at the bedside, private clinics, retail clinics and the developing world.

An engineered membrane to measure electroporation: effect of tethers and bioelectronic interface

This article reports on the construction and predictive models for a platform comprised of an engineered tethered membrane. The platform provides a controllable and physiologically relevant environment for the study of the electroporation process. The mixed self-assembled membrane is formed via a rapid solvent exchange technique. The membrane is tethered to the gold electrode and includes an ionic reservoir separating the membrane and gold surface. Above the membrane, there is an electrolyte solution, and a gold counterelectrode. A voltage is applied between the gold electrodes and the current measured. The current is dependent on the energy required to form aqueous pores and the conductance of each pore. A two-level predictive model, consisting of a macroscopic and a continuum model, is developed to relate the pore dynamics to the measured current. The macroscopic model consists of an equivalent circuit model of the tethered membrane, and asymptotic approximations to the Smoluchowski-Einstein equation of electroporation that is dependent on the pore conductance and the energy required to form aqueous pores. The continuum model is a generalized Poisson-Nernst-Planck (GPNP) system where an activity coefficient to account for steric effects of ions is added to the standard PNP system. The GPNP is used to evaluate the conductance of aqueous pores, and the electrical energy required to form the pores. As an outcome of the setup of the device and the two-level model, biologically important variables can be estimated from experimental measurements. To validate the accuracy of the two-level model, the predicted current is compared with experimentally measured current for different tethering densities.

Efficient single-cell poration by microsecond laser pulses

Payloads including FITC-Dextran dye and plasmids were delivered into NIH/3T3 fibroblasts using microbubbles produced by microsecond laser pulses to induce pores in the cell membranes. Two different operational modes were used to achieve molecular delivery. Smaller molecules, such as the FITC-Dextran dye, were delivered via a scanning-laser mode. The poration efficiency and the cell viability were both 95.1 ± 3.0%. Relatively larger GFP plasmids can be delivered efficiently via a fixed-laser mode, which is a more vigorous method that can create larger transient pores in the cell membrane. The transfection efficiency of 5.7 kb GFP plasmid DNA can reach to 86.7 ± 3.3%. Using this cell poration system, targeted single cells can be porated with high resolution, and cells can be porated in arbitrary patterns.

Cationic peptide exposure enhances pulsed-electric-field-mediated membrane disruption

BACKGROUND

The use of pulsed electric fields (PEFs) to irreversibly electroporate cells is a promising approach for destroying undesirable cells. This approach may gain enhanced applicability if the intensity of the PEF required to electrically disrupt cell membranes can be reduced via exposure to a molecular deliverable. This will be particularly impactful if that reduced PEF minimally influences cells that are not exposed to the deliverable. We hypothesized that the introduction of charged molecules to the cell surfaces would create regions of enhanced transmembrane electric potential in the vicinity of each charged molecule, thereby lowering the PEF intensity required to disrupt the plasma membranes. This study will therefore examine if exposure to cationic peptides can enhance a PEF's ability to disrupt plasma membranes.

METHODOLOGY/PRINCIPAL FINDINGS

We exposed leukemia cells to 40 μs PEFs in media containing varying concentrations of a cationic peptide, polyarginine. We observed the internalization of a membrane integrity indicator, propidium iodide (PI), in real time. Based on an individual cell's PI fluorescence versus time signature, we were able to determine the relative degree of membrane disruption. When using 1-2 kV/cm, exposure to >50 μg/ml of polyarginine resulted in immediate and high levels of PI uptake, indicating severe membrane disruption, whereas in the absence of peptide, cells predominantly exhibited signatures indicative of no membrane disruption. Additionally, PI entered cells through the anode-facing membrane when exposed to cationic peptide, which was theoretically expected.

CONCLUSIONS/SIGNIFICANCE

Exposure to cationic peptides reduced the PEF intensity required to induce rapid and irreversible membrane disruption. Critically, peptide exposure reduced the PEF intensities required to elicit irreversible membrane disruption at normally sub-electroporation intensities. We believe that these cationic peptides, when coupled with current advancements in cell targeting techniques will be useful tools in applications where targeted destruction of unwanted cell populations is desired.

DERIVING AN ELECTRIC CIRCUIT EQUIVALENT MODEL OF CELL MEMBRANE PORES IN ELECTROPORATION

Electroporation is the formation of reversible pores in cell membranes under a brief pulse of high electric field. Dynamics of pore formation during electroporation suggests that the transmembrane potential would settle approximately at the threshold transmembrane potential and the transmembrane resistance would decrease significantly from the state of relaxation. The current electric circuit equivalent models for electroporation containing time-invariant, static and passive components are unable to capture the pore dynamics. A biophysically-inspired electric circuit equivalent model containing dynamic components for membrane pores has been derived using biological parameters. The model contains a voltage-controlled resistor driven by a two-stage cascaded integrator that is activated through a voltage-gated switch. Simulation results with the derived model showed higher accuracy compared to a commonly used model, where the transmembrane resistance decreased million-fold at the onset of electroporation and the transmembrane potential settled at 99.5% of the critical transmembrane potential, thus enabling improved dynamic behavior modeling ability of the pores in electroporation. The derived model allows fast and reliable analysis of this biophysical phenomenon and potentially aids in optimization of various parameters involved in electroporation.

Novel passive element circuits for microdosimetry of nanosecond pulsed electric fields

Microdosimetric models for biological cells have assumed increasing significance in the development of nanosecond pulsed electric field technology for medical applications. In this paper, novel passive element circuits, able to take into account the dielectric dispersion of the cell, are provided. The circuital analyses are performed on a set of input pulses classified in accordance with the current literature. Accurate data in terms of transmembrane potential are obtained in both time and frequency domains for different cell models. In addition, a sensitivity study of the transfer function for the cell geometrical and dielectric parameters has been carried out. This analysis offers a new, simple, and efficient tool to characterize the nsPEFs' action at the cellular level.

Electric field analysis of breast tumor cells

An attractive alternative treatment for malignant tumors that are refractive to conventional therapies, such as surgery, radiation, and chemotherapy, is electrical-pulse-mediated drug delivery. Electric field distribution of tissue/tumor is important for effective treatment of tissues. This paper deals with the electric field distribution study of a tissue model using MAXWELL 3D Simulator. Our results indicate that tumor tissue had lower electric field strength compared to normal cells, which makes them susceptible to electrical-pulse-mediated drug delivery. This difference could be due to the altered properties of tumor cells compared to normal cells, and our results corroborate this.

Single-cell electroporation in Xenopus

Single-cell electroporation (SCE) is a versatile technique for delivering electrically charged macromolecules including DNA, RNA, synthetic oligonucleotides, peptides, dyes, and drugs to individual cells within intact tissues. Here, we describe methods for in vivo-targeted electroporation of single tectal neurons within the albino Xenopus laevis tadpole. Focal electroporation is achieved using a pipette electrode filled with a solution of the delivery molecules and with a tip diameter much smaller than the width of the target cell. The small tip allows for localization of an electric field, which restricts pore formation to only the individual cell in direct contact with the tip. Thus, the small tip permits focal delivery of the charged molecules within the pipette into individual cells. Factors affecting the efficiency of SCE, as well as various applications of this technique, are discussed. Particular focus is directed toward combining SCE with in vivo two-photon microscopy for three-dimensional (3D) imaging of neuron growth and cell-autonomous effects of altered protein function.

Dynamics and control of the two-pulse protocol in electroporation: numerical exploration

Externally applied voltages can create transient, non-selective pores in a cell's membrane, a phenomenon known as electroporation. Electroporation has reduced toxicity, is easy to perform, and does not induce the immune system. Therefore, the technique has a wide range of biological and medical applications. Previous experiments show that a two-pulse protocol, which consists of a fast, large-magnitude pulse and a slow, small-magnitude pulse, can increase the efficiency of drug delivery such as gene electrotransfer. In this work, we investigate the dynamics and control of the two-pulse protocol using a macroscopic model of electroporation. Numerical simulations show that there exists a range of pore radii that cannot be sustained using the conventional, open-loop, two-pulse protocol. As a result, one may need to use pores that are significantly larger than the sizes of the targeted molecules. Moreover, it is not possible to know the rate of delivery a priori. To ensure accurate drug delivery and avoid potential damage to the cell's membrane, we explore feedback mechanisms to eliminate the gap in sustainable pore radii and thus to precisely control the electroporation process. Numerical simulations show that a straightforward feedback algorithm can achieve robust control effects. Moreover, the control algorithm is effective without knowledge of the model and thus has the potential to be implemented in experiments.

Microdosimetry for nanosecond pulsed electric field applications: a parametric study for a single cell

A microdosimetric study of nanosecond pulsed electric fields, including dielectric dispersivity of cell compartments, is proposed in our paper. A quasi-static solution based on the Laplace equation was adapted to wideband signals and used to address the problem of electric field estimation at cellular level. The electric solution was coupled with an asymptotic electroporation model able to predict membrane pore density. An initial result of our paper is the relevance of the dielectric dispersivity, providing evidence that both the transmembrane potential and the pore density are strongly influenced by the choice of modeling used. We note the crucial role played by the dielectric properties of the membrane that can greatly impact on the poration of the cell. This can partly explain the selective action reported on cancerous cells in mixed populations, if one considers that tumor cells may present different dielectric responses. Moreover, these kinds of studies can be useful to determine the appropriate setting of nsPEF generators as well as for the design and optimization of new-generation devices.

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.

Gene electrotransfer: from biophysical mechanisms to in vivo applications : Part 1- Biophysical mechanisms

Electropulsation is one of the nonviral methods successfully used to deliver genes into living cells in vitro and in vivo. This approach shows promise in the field of gene and cellular therapies. The present review focuses on the processes supporting gene electrotransfer in vitro. In the first part, we will report the events occurring before, during, and after pulse application in the specific field of plasmid DNA electrotransfer at the cell level. A critical discussion of the present theoretical considerations about membrane electropermeabilization and the transient structures involved in the plasmid uptake follows in a second part.

The Role of Plasmalemmal-Cortical Anchoring on the Stability of Transmembrane Electropores

The structure of eukaryotic cells is maintained by a network of filamentous actin anchored subjacently to the plasma membrane. This structure is referred to as the actin cortex. We present a locally constrained surface tension model for electroporation in order to address the influence of plasmalemmal-cortical anchoring on electropore dynamics. This model predicts that stable electropores are possible under certain conditions. The existence of stable electropores has been suggested in several experimental studies. The electropore radius at which stability is achieved is a function of the characteristic radii of locally constrained regions about the plasma membrane. This model opens the possibility of using actin-modifying compounds to physically manipulate cortical density, thereby manipulating electroporation dynamics. It also underscores the need to improve electroporation models further by incorporating the influence of trans-electropore ionic and aqueous flow, cortical flexibility, transmembrane protein mobility, and active cellular wound healing mechanisms.

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.

Study of transmembrane potentials on cellular inner and outer membrane--frequency response model and its filter characteristic simulation

Based on the multilayer dielectric model for a spherical cell, a frequency response model of transmembrane potentials on cellular inner and outer membranes is established with a simulating method. The simulating results indicate that transmembrane potential on the inner membrane shows first-order bandpass filter characteristic, while transmembrane potential on the outer membrane shows first-order low-pass filter characteristic approximately. It could be found that the transmembrane potential on the inner membrane is greater than that on the outer membrane, and can keep a higher value in the range from a center frequency to an upper cutoff frequency, which is desirable to induce intracellular electromanipulation. Both a discussion about an equivalent RC model of the cell and the experimental result are in agreement with the aforementioned conclusion. Therefore, the frequency response model could help to choose reasonable window parameters for the application of a nanosecond pulsed electric field to tumor treatment.

Quantification of electroporative uptake kinetics and electric field heterogeneity effects in cells

We have conducted experiments quantitatively investigating electroporative uptake kinetics of a fluorescent plasma membrane integrity indicator, propidium iodide (PI), in HL60 human leukemia cells resulting from exposure to 40 mus pulsed electric fields (PEFs). These experiments were possible through the use of calibrated, real-time fluorescence microscopy and the development of a microcuvette: a specialized device designed for exposing cell cultures to intense PEFs while carrying out real-time microscopy. A finite-element electrostatic simulation was carried out to assess the degree of electric field heterogeneity between the microcuvette's electrodes allowing us to correlate trends in electroporative response to electric field distribution. Analysis of experimental data identified two distinctive electroporative uptake signatures: one characterized by low-level, decelerating uptake beginning immediately after PEF exposure and the other by high-level, accelerating fluorescence that is manifested sometimes hundreds of seconds after PEF exposure. The qualitative nature of these fluorescence signatures was used to isolate the conditions required to induce exclusively transient electroporation and to discuss electropore stability and persistence. A range of electric field strengths resulting in transient electroporation was identified for HL60s under our experimental conditions existing between 1.6 and 2 kV/cm. Quantitative analysis was used to determine that HL60s experiencing transient electroporation internalized between 50 and 125 million nucleic acid-bound PI molecules per cell. Finally, we show that electric field heterogeneity may be used to elicit asymmetric electroporative PI uptake within cell cultures and within individual cells.

Towards solid tumor treatment by irreversible electroporation: intrinsic redistribution of fields and currents in tissue

Local and drug-free tissue treatment by irreversible electroporation (IRE) involves the creation of aqueous pores in a cell's plasma membrane (PM) and leads to non-thermal cell death by necrosis. To investigate explicit pore-based effects we use two-dimensional system models with different spatial scales. The first is a multicellular system model (spatial scale 100 mum) that has irregularly shaped cells, and quantitatively describes dynamic (creation and destruction, evolution in pore size) pore behavior at the PM. The second is a tissue model (spatial scale 200 mm) that is constructed from a unit cell and uses the asymptotic (fixed pore size) electroporation model. Both system models show that significant redistribution of fields and currents occurs through transient PM pores. Pore histograms for the multicellular model demonstrate the simultaneous presence of small and large pores during IRE pulses. The associated significant increase of PM permeability may prove to be essential to understanding how cell death by necrosis occurs. The averaged tissue conductivity in both models increases during IRE pulses because of electroporation. This leads to greater electrical dissipation (heating) and, thus, to larger temperature increases than suggested by tissue models with passive and static electrical properties.

Electrical behavior and pore accumulation in a multicellular model for conventional and supra-electroporation

Extremely large but very short (20 kV/cm, 300 ns) electric field pulses were reported recently to non-thermally destroy melanoma tumors. The stated mechanism for field penetration into cells is pulse characteristic times faster than charge redistribution (displacement currents). Here we use a multicellular model with irregularly shaped, closely spaced cells to show that instead overwhelming pore creation (supra-electroporation) is dominant, with field penetration due to pores (ionic conduction currents) during most of the pulse. Moreover, the model's maximum membrane potential (about 1.2 V) is consistent with recent experimental observations on isolated cells. We also use the model to show that conventional electroporation resulting from 100 microsecond, 1 kV/cm pulses yields a spatially heterogeneous electroporation distribution. In contrast, the melanoma-destroying pulses cause nearly homogeneous electroporation of cells and their nuclear membranes. Electropores can persist for times much longer than the pulses, and are likely to be an important mechanism contributing to cell death.

Modeling electroporation in a single cell

Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.

Singular perturbation analysis of the pore creation transient

Electroporation, in which electric pulses create transient pores in the cell membrane, is an important technique for drug and DNA delivery. Electroporation kinetics is mathematically described by an advection-diffusion boundary value problem. This study uses singular perturbation to derive a reduced description of the pore creation transient in the form of a single integrodifferential equation for the transmembrane voltage Vt. The number of pores and the distribution of their radii are computed from Vt. The analysis contains two nonstandard features: the use of the voltage deviation to peel away the strong exponential dependence of pore creation upon the transmembrane potential, and the autonomous approximation of the pore evolution. Comparing the predictions of the reduced equation with the simulations of the original problem demonstrates that this analysis allows one to predict with good accuracy the number and distribution of pores as a function of the electric pulse strength.

Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation

The recent applications of nanosecond, megavolt-per-meter electric field pulses to biological systems show striking cellular and subcellular electric field induced effects and revive the interest in the biophysical mechanism of electroporation. We first show that the absolute rate theory, with experimentally based parameter input, is consistent with membrane pore creation on a nanosecond time scale. Secondly we use a Smoluchowski equation-based model to formulate a self-consistent theoretical approach. The analysis is carried out for a planar cell membrane patch exposed to a 10 ns trapezoidal pulse with 1.5 ns rise and fall times. Results demonstrate reversible supraelectroporation behavior in terms of transmembrane voltage, pore density, membrane conductance, fractional aqueous area, pore distribution, and average pore radius. We further motivate and justify the use of Krassowska's asymptotic electroporation model for analyzing nanosecond pulses, showing that pore creation dominates the electrical response and that pore expansion is a negligible effect on this time scale.

Inter-pulse interval between rectangular voltage pulses affects electroporation threshold of artificial lipid bilayers

This paper describes experiments that determine how the inter-pulse interval between rectangular pulses in a train of pulses alters the threshold of electroporation of 1-pamitoyl 2-oleoyl phosphatidycholine bilayer lipid membranes. The bilayers were exposed to a train of sixteen 100-micros duration pulses. Threshold voltage and the sequence number of the pulse in the train, where onset of the electroporation occurred, were recorded for six inter-pulse intervals (infinity, 1000 micros, 100 micros, 10 micros, 1 micros, 0 micros). The threshold voltage of the pulse train decreased linearly with the logarithm of the inter-pulse interval. When the inter-pulse interval was 1 microm, electroporation threshold dropped to that of a single pulse with duration 1600 micros (equal to the sum of all pulse durations in the train). In this case, the occurrence of bilayer rupture was almost equally frequent for all pulses in the train. When the inter-pulse interval between the pulses exceeded 1 micros, the influence of the previous pulse on the response to the following pulse declined. It became more likely that the bilayer ruptured during the first half of the train. These experimental observations suggest that a train of pulses applied with short inter-pulse interval (less than 1 ms) can lower the electroporation threshold of bilayer lipid membranes.

Determination of the lipid bilayer breakdown voltage by means of linear rising signal

Electroporation is characterized by formation of structural changes within the cell membrane, which are caused by the presence of electrical field. It is believed that "pores" are mostly formed in lipid bilayer structure; if so, planar lipid bilayer represents a suitable model for experimental and theoretical studies of cell membrane electroporation. The breakdown voltage of the lipid bilayer is usually determined by repeatedly applying a rectangular voltage pulse. The amplitude of the voltage pulse is incremented in small steps until the breakdown of the bilayer is obtained. Using such a protocol each bilayer is exposed to a voltage pulse many times and the number of applied voltage pulses is not known in advance. Such a pre-treatment of the lipid bilayer affects its stability and consequently the breakdown voltage of the lipid bilayer. The aim of this study is to examine an alternative approach for determination of the lipid bilayer breakdown voltage by linear rising voltage signal. Different slopes of linear rising signal have been used in our experiments (POPC lipids; folding method for forming in the salt solution of 100 mM KCl). The breakdown voltage depends on the slope of the linear rising signal. Results show that gently sloping voltage signal electroporates the lipid bilayer at a lower voltage then steep voltage signal. Linear rising signal with gentle slope can be considered as having longer pre-treatment of the lipid bilayer; thus, the corresponding breakdown voltage is lower. With decreasing the slope of linear rising signal, minimal breakdown voltage for specific lipid bilayer can be determined. Based on our results, we suggest determination of lipid bilayer breakdown voltage by linear rising signal. Better reproducibility and lower scattering are obtained due to the fact that each bilayer is exposed to electroporation treatment only once. Moreover, minimal breakdown voltage for specific lipid bilayer can be determined.

Microdosimetry for conventional and supra-electroporation in cells with organelles

Conventional electroporation (EP) by 0.1 to 1 kV/cm pulses longer than 100 micros, and supra-electroporation by 10 to 300 kV/cm pulses shorter than 1 micros cause different cellular effects. Conventional EP delivers DNA, proteins, small drugs, and fluorescent indicators across the plasma membrane (PM) and causes moderate levels of phosphatidylserine (PS) translocation at the PM. We hypothesize that supra-EP is central to intracellular effects such as apoptosis induction and higher levels of PS translocation. Our cell system model has 20,000 interconnected local models for small areas of the PM and organelle membranes, small regions of aqueous media, appropriate resting potentials, and the asymptotic EP model. Conventional EP primarily affects the PM, but with a hint of endoplasmic reticulum involvement. Supra-EP can involve all of a cell's membrane at the largest fields. Conventional EP fields tend to go around cells, but supra-EP fields go through cells, extensively penetrating organelles.

Fluorescence microscopy imaging of electroperturbation in mammalian cells

We report the design, integration, and validation of a fluorescence microscopy system for imaging of electroperturbation--the effects of nanosecond, megavolt-per-meter pulsed electric fields on biological cells and tissues. Such effects have potential applications in cancer therapy, gene regulation, and biophysical research by noninvasively disrupting intracellular compartments and inducing apoptosis in malignant cells. As the primary observing platform, an epifluorescence microscope integrating a nanosecond high-voltage pulser and a micrometer electrode chamber enable in situ imaging of the intracellular processes triggered by high electric fields. Using specific fluorescence molecular probes, the dynamic biological responses of Jurkat T lymphocytes to nanosecond electric pulses (nanoelectropulses) are studied with this system, including calcium bursts, the polarized translocation of phosphatidylserine (PS), and nuclear enlargement and chromatin/DNA structural changes.

Membrane electroporation theories: a review

Electroporation, the transient increase in the permeability of cell membranes when exposed to a high electric field, is an established in vitro technique and is used to introduce DNA or other molecules into cells. When the trans-membrane voltage induced by an external electric field exceeds a certain threshold (normally 0.2-1 V), a rearrangement of the molecular structure of the membrane occurs, leading to pore formation in the membrane and a considerable increase in the cell membrane permeability to ions, molecules and even macromolecules. This phenomenon is, potentially, the basis for many in vivo applications such as electrochemotherapy and gene therapy, but still lacks a comprehensive theoretical basis. This article reviews the state of current electroporation theories and briefly considers current and potential applications in biology and medicine.