Electroporation Model Research Articles

Asymmetric insertion of membrane proteins in lipid bilayers by solid-state NMR paramagnetic relaxation enhancement: a cell-penetrating Peptide example.

A novel solid-state NMR technique for identifying the asymmetric insertion depths of membrane proteins in lipid bilayers is introduced. By applying Mn (2+) ions on the outer but not the inner leaflet of lipid bilayers, the sidedness of protein residues in the lipid bilayer can be determined through paramagnetic relaxation enhancement (PRE) effects. Protein-free lipid membranes with one-side Mn (2+)-bound surfaces exhibit significant residual (31)P and lipid headgroup (13)C intensities, in contrast to two-side Mn (2+)-bound membranes, where lipid headgroup signals are mostly suppressed. Applying this method to a cell-penetrating peptide, penetratin, we found that at low peptide concentrations, penetratin is distributed in both leaflets of the bilayer, in contrast to the prediction of the electroporation model, which predicts that penetratin binds to only the outer lipid leaflet at low peptide concentrations to cause an electric field that drives subsequent peptide translocation. The invalidation of the electroporation model suggests an alternative mechanism for intracellular import of penetratin, which may involve guanidinium-phosphate complexation between the peptide and the lipids.

A discontinuous Galerkin method for elliptic interface problems with application to electroporation

AbstractWe solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L2‐norm. We apply our method to the numerical study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright © 2008 John Wiley & Sons, Ltd.

A propagating heat wave model of skin electroporation

The main barrier to transdermal drug delivery in human skin is the stratum corneum. Pulsed electric fields (PEFs) of sufficient amplitude can create new aqueous pathways across this barrier and enhance drug delivery through the skin. Here, we describe a model of pore formation between adjacent corneocytes that predicts the following sequence of events: (1) the PEF rapidly charges the stratum corneum near the electrode until the transepidermal potential difference is large enough to drive water into a small region of the stratum corneum, creating new aqueous pathways. (2) PEFs then drive a high current density through this newly created electropore to generate Joule heating that warms the pore perimeter. (3) This temperature rise at the perimeter increases the probability of further electroporation there as the local sphingolipids reach their phase transition temperature. (4) This heat-generated wave of further electroporation propagates outward until the surface area of the pore becomes so large that the reduced current density no longer generates sufficient heat to reach the phase transition temperature of the sphingolipids. (5) Cooling and partial recovery occurs after the field pulse. This process yields large, high permeability regions in the stratum corneum at which molecules can more readily cross this skin barrier. We present a model for this process that predicts that the initial radius of the first aqueous pathway is approximately 5 nm for a transdermal voltage of 60 V at room temperature.

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.

Mathematical Modeling of Irreversible Electroporation for Treatment Planning

Irreversible Electroporation (IRE) is a new drug-free method to ablate undesirable tissue of particular use in cancer therapy. IRE achieves cell death within the targeted tissue through a series of electric pulses that elevate the transmembrane potentials to an extent that permanently damages the lipid bilayers throughout the treated region. Although the IRE procedure is easy to perform, treatment planning is complicated by the fact that the electric field distribution within the tissue, the greatest single factor controlling the extents of IRE, depends non-trivially on the electrode configuration, pulse parameters and any tissue heterogeneities. To address this difficulty, we instruct on how to properly model IRE and discuss the benefit of modeling in designing treatment protocols. The necessary theoretical basis is introduced and discussed through the detailed analysis of two classic dual-electrode configurations from electrochemotherapy: coaxial disk electrodes and parallel needle electrodes. Dimensionless figures for these cases are also provided that allow cell constants, treated areas, and the details of heating to be determined for a wide range of conditions, for uniform tissues, simply by plugging in the appropriate physical property values and pulse parameters such as electrode spacing, size, and pulse amplitude. Complexities, such as heterogeneous tissues and changes in conductivity due to electroporation, are also discussed. The synthesis of these details can be used directly by surgeons in treatment planning. Irreversible electroporation is a promising new technique to treat cancer in a targeted manner without the use of drugs; however, it does require a detailed understanding of how electric currents flow within biological tissues. By providing the understanding and tools necessary to design an IRE protocol, this study seeks to facilitate the translation of this new and exciting cancer therapy into clinical practice.

Non-linear time domain model of electropermeabilization: Response of a single cell to an arbitrary applied electric field

Background: Electroporation is now a common tool in biotechnology and is used in a number of medical treatments. Until recently, the development of theoretical models of electroporation has lagged behind the experimental research. In order to optimize the efficiency of electroporation, it is important to consider as many biological and physical aspects as possible and it is a necessity that a variety of electric pulse parameters be tried. Thus a comprehensive model which can predict electropermeabilization as a result of any form of applied electric field and other important electroporation parameters is necessary. Results: A numerical model for a single cell electroporated by application of arbitrary external electric field pulses has been developed. The model is used to compare the transmembrane potential Vm, and pore density N, developed in response to the pulses. Vm and N are calculated via a piece-wise step response method that enables solutions to be obtained for any practical applied electric field waveform. Pore density is shown to increase so long as a threshold Vm is maintained by the electric field, and effectively clamps Vm to just over 1 V while N is increasing. Short unipolar pulses are also shown to create asymmetrical N between the two cell polar regions, whereas bipolar pulses result in a symmetrical N. Conclusions: The model presented here helps predict dynamic non-linear results of electropermeabilization, given any form of applied electric field and other important electroporation system parameters. This model can be used as a tool for the determination of starting parameters in biological applications.

Local Temperature Rises Influence In Vivo Electroporation Pore Development: A Numerical Stratum Corneum Lipid Phase Transition Model

Electroporation is an approach used to enhance transdermal transport of large molecules in which the skin is exposed to a series of electric pulses. Electroporation temporarily destabilizes the structure of the outer skin layer, the stratum corneum, by creating microscopic pores through which agents, ordinarily unable to pass into the skin, are able to pass through this outer barrier. Long duration electroporation pulses can cause localized temperature rises, which result in thermotropic phase transitions within the lipid bilayer matrix of the stratum corneum. This paper focuses on electroporation pore development resulting from localized Joule heating. This study presents a theoretical model of electroporation, which incorporates stratum corneum lipid melting with electrical and thermal energy equations. A transient finite volume model is developed representing electroporation of in vivo human skin, in which stratum corneum lipid phase transitions are modeled as a series of melting processes. The results confirm that applied voltage to the skin results in high current densities within the less resistive regions of the stratum corneum. The model captures highly localized Joule heating within the stratum corneum and subsequent temperature rises, which propagate radially outward. Electroporation pore development resulting from the decrease in resistance associated with lipid melting is captured by the lipid phase transition model. As the effective pore radius grows, current density and subsequent Joule heating values decrease.

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 μs), creation of pores (0.51–1.43 μs), and evolution of pore radii (1.43 μs to 1 ms). This pulse creates ∼341,000 pores, of which 97.8% are small (≈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.

Modeling Environment for Numerical Simulation of Applied Electric Fields on Biological Cells

The application of electric pulses in cells increases membrane permeability. This phenomenon is called electroporation. Current electroporation models do not explain all experimental findings: part of this problem is due to the limitations of numerical methods. The Equivalent Circuit Method (ECM) was developed in an attempt to solve electromagnetic problems in inhomogeneous and anisotropic media. ECM is based on modeling of the electrical transport properties of the medium by lumped circuit elements as capacitance, conductance, and current sources, representing the displacement, drift, and diffusion current, respectively. The purpose of the present study was to implement a 2-D cell Model Development Environment (MDE) of ionic transport process, local anisotropy around cell membranes, biological interfaces, and the dispersive behaviour of tissues. We present simulations of a single cell, skeletal muscle, and polygonal cell arrangement. Simulation of polygonal form indicates that the potential distribution depends on the geometrical form of cell. The results demonstrate the importance of the potential distributions in biological cells to provide strong evidences for the understanding of electroporation.

Increased immunogenicity of HIV vaccination with constant-current electroporation and molecular adjuvants in mice and rhesus macaques

DNA vaccine studies in primates have yet to achieve the levels of immunogenicity predicted by mouse models. As a result, there have been numerous studies investigating various methods to increase the immunogenicity of DNA vaccines. Accordingly we have examined the ability of low trauma constant-current electroporation(CCEP) and molecular adjuvants to facilitate the immune responses induced by DNA vaccination. In mice we compared intramuscular (IM) injection alone with IM injection followed by CCEP DNA delivery. We observed increased cellular and humoral responses in electroporated mice using 20 fold less DNA than mice receiving DNA by IM injection alone. Further, we observed enhanced cytotoxic responses using molecular adjuvants in a skin electroporation model over electroporation alone. We subsequently performed a macaque study comparing immunizations of HIV gag and env DNA with or without CCEP. We found that CCEP additively enhanced cellular immune response and increased HIV gag antibody titers 5 fold in vaccinated macaques. Furthermore, CCEP can be improved with the addition of molecular adjuvants resulting in immune responses that mimic those induced by viral vectors. These results have important implications for HIV vaccines and immunotherapy.

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.

The Spatially Distributed Dynamic Transmembrane Voltage of Cells and Organelles due to 10 ns Pulses: Meshed Transport Networks

The authors describe two versions of a two-dimensional (2-D) cell model that contains three circular membranes representing the plasma membrane (PM) and single bilayer approximations to both the nuclear envelope and the mitochondrial membrane. The first version uses a Cartesian transport network, which respects topology but approximates geometry. The second version uses a meshed transport network, which respects both. The asymptotic electroporation model is assigned to all local membrane sites in order to assess the electrical response of the membranes. The predictions of these two models are presented for 10-ns trapezoidal pulses with 1.5 ns rise and fall times. The applied field magnitudes range from 1 to 100 kV/cm, corresponding to recent experiments. The spatially distributed electroporation models exhibit a supraelectroporation for the larger pulses with a maximum transmembrane voltage of Um~1.5 V for both the PM and organelle membranes. For the larger fields, the PM and organelle membranes electroporate essentially simultaneously. The meshed version of the transport network eliminates numerical artifacts and is more computationally efficient

Physical modelling of electroporation in close cell-to-cell proximity environments

Many applications of electroporation, especially those utilizing electrofusion and in-vivo electroporation, involve cell environments that include close cell-to-cell proximity and a wide range of target cell size. It is important to understand how this kind of environment may alter optimum electroporation electrical parameters for any given application. A physical, electrically equivalent model of biological cell electroporation, based on aqueous solution filled thin latex rubber membrane spheroids, was used to investigate membrane permeabilization behaviour where there is both close cell-to-cell proximity and different cell radii. Cell model arrangements were pulsed using either a 50 µs or 10 µs, 1/e decay time constant dc capacitive discharge electric field, with peak amplitudes of 160–500 kV m−1. Results indicate that, compared to cells in isolation, electroporation initiates at substantially decreased applied electric field magnitudes in regions of close cell-to-cell proximity where the external media conductivity is lower than the cell interior conductivity, and the membrane is maximally polarized. Additionally, the use of shorter time constant, higher peak magnitude pulse parameters should reduce the relative difference in threshold membrane permeabilization in regions of close cell-to-cell proximity for cells of different size so that the degree of electroporation is more uniform for variable size and shape target cell populations.

Microdosimetry for conventional and supra-electroporation in cells with organelles

Conventional electroporation (EP) by 0.1 to 1 kV/cm pulses longer than 100 μs, and supra-electroporation by 10 to 300 kV/cm pulses shorter than 1 μs 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.

Effect of the Electroporation in the Field Calculation in Biological Tissues

This article presents results from the field calculation in a model of biological tissue taking into account the electroporation process. The electroporation model used in this study was proposed and experimentally verified by Glaser et al. for planar membranes. The numerical method for field calculation is based on a two-step process: (1) a cell-scale analysis, used for obtaining the field and current in a small volume containing only one cell and its nearest neighbors; and (2) a tissue-scale analysis, based on averaged values of conductivity and permittivity (obtained from the cell-scale analysis) and used for field calculation in a large volume of the tissue. The results for a high voltage applied between two electrodes in a two-dimensional analysis show that the electric field in the porated tissue extends beyond the limits obtained when the electroporation process is not taken into account. Furthermore, due to the electroporation, the tissue conductivity increases in the space between the electrodes. These results show that the electroporation process cannot be ignored in the field calculation in biological tissues when high strength electric fields are present.

Transport Lattice Approach to Describing Cell Electroporation: Use of a Local Asymptotic Model

Electroporation has been widely used to manipulate cells and tissues, but quantitative understanding of electrical behavior in cell membranes has not been achieved. According to the transient aqueous pore hypothesis, pore creation and expansion is a nonlinear, hysteretic process. Different membrane sites respond locally to their own transmembrane voltage history, so that a self-consistent description should involve the interaction of many different regions of a cell membrane model and its aqueous electrolytes. A transport lattice system model of a cell allows active and passive interaction models for local transport and storage of charge to be combined, yielding approximate solutions for this highly interacting system. Here, we use an asymptotic model for local membrane electroporation, which involves solving an ordinary differential equation for each local membrane area of the system model, subject to constraints imposed by self-consistency throughout the system model of the cell. To illustrate this approach, we first treat a model for a space- and voltage-clamped skeletal muscle cell. We then create and analyze models of a circular cell and of a budding yeast cell pair, both of which exhibit electroporation when exposed to pulsed electric fields.

Model of Creation and Evolution of Stable Electropores for DNA Delivery

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.

144. Duration of Reporter Gene Expression from Naled pDNA in the Mouse Lung Following Direct Electroporation and Development or Wire Electrodes for Sheep Lung Electroporation Studies

Current non-viral vectors for lung gene transfer are limited by inefficient uptake, and low levels of expression in cells throughout the lung. The use of electroporation to enhance reporter gene expression from naked plasmid DNA (pDNA) in the mouse lung has been assessed. A direct electroporation model has been established, in which following delivery of pDNA and electroporation of the left lung, luciferase (Lux) reporter gene expression has been enhanced by up to 500 fold compared to the non-electroporated right lung depending on the combination of plasmid, field strength (V/cm) and pulse length employed. Furthermore, following delivery of a GFP expressing plasmid, up to 5% of the left lung cells were positive for GFP after electroporation. Now, the duration of Lux activity following electroporation of the mouse lung has been assessed. Female BALB/c mice were anaesthetised with isoflurane and received 100μg pUbLux (human ubiquitin C promoter, Lux transgene) in 150μl water. The left lungs of mice were exposed by performing a lateral thoracotomy. Electroporation of the left lung (8 pulses of 800V/cm, 2ms with a 1sec interval) was carried out using the BTX ECM®830 Generator with 2-Needle electrodes with 5mm gap with the right lungs remaining non-electroporated. Lux activity was measured at 2, 14 and 28 days post dosing. At day 2 post dosing, mean Lux activity in the left lungs of mice was 40 fold higher than the right lung (Mann-Whitney U: P = 0.016). The Lux activity in the left lungs at day 28 post dosing was no different to the level at day 2 (P=0.512) and still significantly higher than the activity observed in the right lung (P = 0.050). Therefore this study has established that direct electroporation of the mouse lung can result in high levels of Lux activity from naked pDNA and that this level persists for at least 28 days post dosing. In similar studies with the plasmid pCIKLux (CMV promoter, Lux transgene), electroporation resulted in far greater levels of expression at day 2 post dosing, but by day 14, the Lux activity had fallen to background. The safety and efficacy of lung electroporation has therefore been well established in the mouse lung. Further development of lung electroporation is now planned in the sheep lung, as a larger animal model will be more relevant for clinical development of this approach. A series of wire electrodes have been constructed from Teflon insulated stainless steel up to 80cm in length with a diameter of just 0.3mm. In an ex vivo mouse lung model, electroporation with these wires following pCIKLux intranasal delivery (100μg pDNA/150μl) resulted in equivalent 200 fold increases in Lux activity to commercially available needle electrodes. These wire electrodes will be placed within the sheep airways with a bronchoscope allowing for a range of electroporation studies to be carried out. These studies will determine if the electric field can be efficiently and safely applied over a large area to allow electroporation to be used for improving gene transfer throughout the whole lung.

A model for bilayer membrane electroporation based on resultant electromechanical stress

Reconsideration of the effect of an electrical field applied across a phospholipid bilayer membrane shows that, in addition to a compressive stress normal to the membrane plane, transverse traction stresses are generated in the lateral plane of the membrane. In the fields usually employed for electroporation these transverse stresses are likely to be sufficient to reduce the membrane tension considerably, causing electroporation and rupture. This mode of field-induced change in the membrane provides a natural model for the various forms of electroporation.

Dynamical modeling of cellular response to short-duration, high-intensity electric fields

The interaction of ultra-short duration, high-intensity electric fields with biological cells has recently begun to generate significant interest due to the possibility for non-thermal manipulation of cellular functions. It is clear that a full understanding requires a dynamical model for both electroporation and the electrostatic potential evolution. Here, dynamical aspects related to electroporation are reviewed. The simple model used in the literature is somewhat incorrect and unphysical for a variety of reasons. Our model for the pore formation energy, E(r), includes a dependence on pore population, density, a variable surface tension, and is dynamic in nature. It is shown that membranes can survive a strong electric pulse and recover provided the pore distribution has a relatively large spread. If, however, the population consists predominantly of larger radii pores, then irreversibility can result. Physically, such a distribution could arise if pores at adjacent sites coalesce. Results show that a finite time delay exists for pore formation, and can lead to a transient overshoot of the transmembrane potential V/sub mem/ beyond 1.0 V. Pore re-sealing is shown to consist of an initial fast process, a 10/sup -4/ s delay, followed by a much slower closing at a time constant of about 10/sup -1/ s. This establishes a time-window for effective killing by a second pulse.