A Theoretical Study of Single-Cell Electroporation in a Microchannel

Electroporation of a single cell in a microchannel was studied. The effects of electrical (e.g., strength of the electric pulse) and geometrical (e.g., microchannel height, electrode size and position) parameters on cell membrane permeabilization were investigated. The electrodes were assumed to be embedded in the walls of the microchannel; the cell was suspended between these two electrodes. By keeping the electric pulse constant, increasing the microchannel height reduces the number and the radius of the biggest nanopores, as well as the electroporated area of the cell membrane. If the width of the electrodes is bigger than the cell diameter, the transmembrane potential will be centralized and have a sinusoidal distribution around the cell if nanopores are not generated. As the width of the electrode decreases and becomes smaller than the cell diameter, the local transmembrane potential decreases; in the nonelectroporative area, the transmembrane potential distribution deviates from the sinusoidal behavior; the induced transmembrane potential also concentrates around the poles of the cell membrane (the nearest points of the cell membrane to the electrodes). During cell membrane permeabilization, the biggest nanopores are initially created at the poles and then the nanopore population expands toward the equator. The number of the created nanopores reaches its maximal value within a few microseconds; further presence of the electric pulse may not influence the number and location of the created nanopores anymore but will develop the generated nanopores. Strengthening the electric pulse intensifies the size and number of the created nanopores as well as the electroporated area on the cell membrane.     

Time-dependent interfacial charging effects of electrical fields applied to biological systems

An important aspect of the interaction of a biological system with an externally produced electric field is that of charge separation and interfacial charging. This aspect has been ignored in some recent experimental and theoretical work. In the case of small regions of lower electrical resistivity imbedded in a higher resistivity medium, charge separation across the lower resistivity regions will result in charging of the interfaces between the lower and higher resistivity regions. The field produced by this charge separation will significantly affect the shape and the magnitude of the net electric field pulse within the lower resistivity regions. In particular, the field experienced by bone cells will be quite different from the externally produced field. The shape as well as the magnitude of the net electric field experienced by the cells depends on the time rate of change of the rising and falling phases of the externally produced electric field pulse.     

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.     

Early stage shape change of human erythrocytes after application of electric field pulses.

Erythrocytes which receive electric field pulses are subject to poration, fusion and shape changes due to electrodynamic forces, aminophospholipid perturbation and influences on the normal flip-flop process. The shape change characteristics of cells suspended in different media were analysed after application of rectangular electric field pulses from t=11-44 micros and from E=4-8 kV/cm. Albumin is shown to decelerate the echinocyte shape change within the first few seconds after pulse application. The addition of fluoride and vanadate accelerates the shape change due to their inhibiting influence on the aminophospholipid translocase. For both the duration of the field pulse and its field strength, there exist lower threshold values under which no early stage shape change is observable. The activation energy calculated from the dissipative influence of the electric field alone is smaller than expected, indicating the electrodynamic influence on the flip-flop process. Cell shapes were additionally analysed by contour tracing to focus on the echinocyte spicule distribution after pulse application. This image analysis revealed that, with an increase of both pulse duration and field strength, the shape change velocity and the shape change intensity increase.     

Effects of pulsed electric fields on mouse spleen lymphocytes in vitro

The effects of pulsed electric fields on cell membranes were investigated. In vitro exposure of mouse splenocytes to a single high-voltage pulse resulted in an increase in membrane permeability that was dependent on both the electric field strength and the pulse duration. Exposure to a 2 μs, 3.0 kV/cm pulse resulted in the induction of a 1.26 V transmembrane potential, and elicited a 50% loss of intracellular K⁺. These results are in agreement with previous studies of the effects of pulsed electric fields on erythrocytes and microorganisms. The effect of pulsed electric fields on the functional integrity of lymphocytes was i vestigated by measuring [³H]thymidine incorporation by cells cultured in the presence and absence of various mitogens following exposure to an electrical pulse. No statistically significant effects on the response of mouse spleen lymphocytes to concanavalin A, phytohemagglutinin or lipopolysaccharide were observed following exposure to 2 μs electric pulses at amplitudes of up to 3.5 kV/cm. Exposure to a single 10 μs pulse of 2.4–3.5 kV/cm produced a statistically significant reduction in the response of lymphocytes to lipopolysaccharide stimulation that was attributed to cell death.     

The effects of an electric field on soluble collagen.

Electric birefringence decay curves of collagen suspended in aqueous buffered media were plotted as functions of pulse width and amplitude. They were then resolved into two components by means of an analog simulator. When these data were combined with the results of repeated pulsing, it was shown that an electric field promotes aggregation of collagen, although the variety of aggregate sizes falls within a fixed range. Observations of electric birefringence of dissolved collagen preparations as a function of ionic strengths tend to indicate that the bonding that occurs in an electric field is electrostatic.     

The shapes of backbones of chain molecules: Three-dimensional characterization by spherical shape maps

In this work we present a new method to characterize the shape of flexible chain molecules. The procedure associates a sphere and a spherical shape map with each given molecular backbone. Each point on the sphere is classified according to the crossing pattern obtained when the backbone is looked at along a direction defined by the center of the sphere and the chosen point. The approach is simple to implement. It consists of the following steps: (a) enclosing the backbone by a sphere, whose center is the geometrical center of the backbone; (b) projecting the backbone onto a plane tangent to the sphere at the given point; and (c) characterizing the resulting planar curve by a vector specifying the number and handedness type of the crossings. When the procedure is repeated for all points on the spherical surface, the latter is divided into regions that are equivalence classes of points, corresponding to directions from where the backbone has the same overcrossing pattern. The computation of these equivalence classes is performed automatically by the computer, by determining the boundary of the regions characterized by different crossing vectors. The characterization provided is thus direction independent since it takes into account all possible directions from where a backbone can be analyzed. The procedure is illustrated for a number of supersecondary protein structures and small proteins. We find that a characterization of substructures can be obtained in terms of the arrangement of the equivalence region for the viewing directions from where the backbone shows no crossings. For instance, an α-helix is represented by a spherical map with a small “band” region of no crossings perpendicular to the helical axis. Other supersecondary structural features are described in a similar fashion. A number of refinements of the method, based on the distances between crossings, are also given for the case of irregular backbones. © 1992 John Wiley & Sons, Inc.     

A microfluidic biochip for the nanoporation of living cells

This paper deals with the development of a microfluidic biochip for the exposure of living cells to nanosecond pulsed electric fields (nsPEF). When exposed to ultra short electric pulses (typical duration of 3-10ns), disturbances on the plasma membrane and on the intra cellular components occur, modifying the behavioral response of cells exposed to drugs or transgene vectors. This phenomenon permits to envision promising therapies. The presented biochip is composed of thick gold electrodes that are designed to deliver a maximum of energy to the biological medium containing cells. The temporal and spectral distributions of the nsPEF are considered for the design of the chip. In order to validate the fabricated biochip ability to orient the pulse towards the cells flowing within the exposition channels, a frequency analysis is provided. High voltage measurements in the time domain are performed to characterize the amplitude and the shape of the nsPEF within the exposition channels and compared to numerical simulations achieved with a 3D Finite-Difference Time-Domain code. We demonstrate that the biochip is adapted for 3 ns and 10 ns pulses and that the nsPEF are homogenously applied to the biological cells regardless their position along the microfluidic channel. Furthermore, biological tests performed on the developed microfluidic biochip permit to prove its capability to permeabilize living cells with nanopulses. To the best of our knowledge, we report here the first successful use of a microfluidic device optimized for the achievement and real time observation of the nanoporation of living cells.     

Electrostatic modeling of ion pores. Energy barriers and electric field profiles

This paper presents calculations of the image potential for an ion in an aqueous pore through lipid membrane and the electric field produced in such a pore when a transmembrane potential is applied. The method used is one introduced by Levitt (1978, Biophys. J. 22:209), who solved an equivalent problem, in which a surface charge density is placed at the dielectric boundary. It is shown that there are singularities in this surface charge density if the model system has sharp corners. Numerically accurate calculations require exact treatment of these singularities. The major result of this paper is the development of a projection method that explicitly accounts for this behavior. It is shown how this technique can be used to compute, both reliably and efficiently, the electrical potential within a model pore in response to any electrical source. As the length of a channel with fixed radius is increased, the peak in the image potential approaches that of an infinitely long channel more rapidly than previously believed. When a transmembrane potential is applied the electric field within a pore is constant over most of its length. Unless the channel is much longer than its radius, the field extends well into the aqueous domain. For sufficiently dissimilar dielectrics the calculated values for the peak in the image potential and for the field well within the pore can be summarized by simple empirical expressions that are accurate to within 5%.     

Voltage profile along the permeation pathway of an open channel

For ion channels, the transmembrane potential plays a critical role by acting as a driving force for permeant ions. At the microscopic level, the transmembrane potential is thought to decay nonlinearly across the ion permeation pathway because of the irregular three-dimensional shape of the channel's pore. By taking advantage of the current structural and functional understanding of cyclic nucleotide-gated channels, in this study we experimentally explore the transmembrane potential's distribution across the open pore. As a readout for the voltage drop, we engineered cysteine residues along the selectivity filter and scanned the sensitivity of their modification rates by Ag⁺ to the transmembrane potential. The experimental data, which indicate that the majority of the electric field drops across the selectivity filter, are in good agreement with continuum electrostatic calculations using a homology model of an open CNG channel. By focusing the transmembrane potential across the selectivity filter, the electromotive driving force is coupled with the movement of permeant ions in the filter, maximizing the efficiency of this process.     

Electric Field-Induced Transmembrane Potential Depends on Cell Density and Organizatio

Electrochemotherapy is a novel technique to enhance the delivery of chemotherapeutic drugs into tumor cells. In this procedure, electric pulses are delivered to cancerous cells, which induce membrane permeabilization, to facilitate the passage of cytotoxic drugs through the cell membrane. This study examines how electric fields interact with and polarize a system of cells. Specifically, we consider how cell density and organization impact on induced cell transmembrane potential due to an external electric field. First, in an infinite volume of spherical cells, we examined how cell packing density impacts on induced transmembrane potential. With high cell density, we found that maximum induced transmembrane potential is suppressed and that the transmembrane potential distribution is altered. Second, we considered how orientation of cell sheets and strands, relative to the applied field, affects induced transmembrane potential. Cells that are parallel to the field direction suppress induced transmembrane potential, and those that lie perpendicular to the applied field potentiate its effect. Generally, we found that both cell density and cell organization are very important in determining the induced transmembrane potential resulting from an applied electric field.     

Effect of Blood Vessel Segmentation on the Outcome of Electroporation-Based Treatments of Liver Tumors

Electroporation-based treatments rely on increasing the permeability of the cell membrane by high voltage electric pulses applied to tissue via electrodes. To ensure that the whole tumor is covered with sufficiently high electric field, accurate numerical models are built based on individual patient anatomy. Extraction of patient''s anatomy through segmentation of medical images inevitably produces some errors. In order to ensure the robustness of treatment planning, it is necessary to evaluate the potential effect of such errors on the electric field distribution. In this work we focus on determining the effect of errors in automatic segmentation of hepatic vessels on the electric field distribution in electroporation-based treatments in the liver. First, a numerical analysis was performed on a simple ''sphere and cylinder'' model for tumors and vessels of different sizes and relative positions. Second, an analysis of two models extracted from medical images of real patients in which we introduced variations of an error of the automatic vessel segmentation method was performed. The results obtained from a simple model indicate that ignoring the vessels when calculating the electric field distribution can cause insufficient coverage of the tumor with electric fields. Results of this study indicate that this effect happens for small (10 mm) and medium-sized (30 mm) tumors, especially in the absence of a central electrode inserted in the tumor. The results obtained from the real-case models also show higher negative impact of automatic vessel segmentation errors on the electric field distribution when the central electrode is absent. However, the average error of the automatic vessel segmentation did not have an impact on the electric field distribution if the central electrode was present. This suggests the algorithm is robust enough to be used in creating a model for treatment parameter optimization, but with a central electrode.     

High-frequency irreversible electroporation (H-FIRE) for non-thermal ablation without muscle contraction

Background

Therapeutic irreversible electroporation (IRE) is an emerging technology for the non-thermal ablation of tumors. The technique involves delivering a series of unipolar electric pulses to permanently destabilize the plasma membrane of cancer cells through an increase in transmembrane potential, which leads to the development of a tissue lesion. Clinically, IRE requires the administration of paralytic agents to prevent muscle contractions during treatment that are associated with the delivery of electric pulses. This study shows that by applying high-frequency, bipolar bursts, muscle contractions can be eliminated during IRE without compromising the non-thermal mechanism of cell death.

Methods

A combination of analytical, numerical, and experimental techniques were performed to investigate high-frequency irreversible electroporation (H-FIRE). A theoretical model for determining transmembrane potential in response to arbitrary electric fields was used to identify optimal burst frequencies and amplitudes for in vivo treatments. A finite element model for predicting thermal damage based on the electric field distribution was used to design non-thermal protocols for in vivo experiments. H-FIRE was applied to the brain of rats, and muscle contractions were quantified via accelerometers placed at the cervicothoracic junction. MRI and histological evaluation was performed post-operatively to assess ablation.

Results

No visual or tactile evidence of muscle contraction was seen during H-FIRE at 250 kHz or 500 kHz, while all IRE protocols resulted in detectable muscle contractions at the cervicothoracic junction. H-FIRE produced ablative lesions in brain tissue that were characteristic in cellular morphology of non-thermal IRE treatments. Specifically, there was complete uniformity of tissue death within targeted areas, and a sharp transition zone was present between lesioned and normal brain.

Conclusions

H-FIRE is a feasible technique for non-thermal tissue ablation that eliminates muscle contractions seen in IRE treatments performed with unipolar electric pulses. Therefore, it has the potential to be performed clinically without the administration of paralytic agents.     

Measurement of mitochondrial transmembrane electric potential using the fluorescent probe DSM]

The measurement of transmembrane electric potential of rat liver mitochondria was performed with fluorescent probe DSM. In the incubation medium with succinate the electric potential was -190 +/- 5 mV. Complete uncoupling caused by CCCP in the concentration 0.5 microM decreased the potential to -142 +/- 3 mV. In the partial uncoupling with a half of the mentioned CCCP concentration the potential was -158 +/- 6 mV. DSM influence on oxidation and phosphorylation was not detected.     

Influence of the crash pulse shape on the peak loading and the injury tolerance levels of the neck in in vitro low-speed side-collisions

The aim of the present in vitro study was to investigate the effect of the crash pulse shape on the peak loading and the injury tolerance levels of the human neck. In a custom-made acceleration apparatus 12 human cadaveric cervical spine specimens, equipped with a dummy head, were subjected to a series of incremental side accelerations. While the duration of the acceleration pulse of the sled was kept constant at 120 ms, its shape was varied: Six specimens were loaded with a slowly increasing pulse, i.e. a low loading rate, the other six specimens with a fast increasing pulse, i.e. a high loading rate. The loading of the neck was quantified in terms of the peak linear and angular acceleration of the head, the peak shear force and bending moment of the lower neck and the peak translation between head and sled. The shape of the acceleration curve of the sled only seemed to influence the peak translation between head and sled but none of the other four parameters. The neck injury tolerance level for the angular acceleration of the head and for the bending moment of the lower neck was almost identical for both, the high and the low loading rate. In contrast, the injury tolerance level for the linear acceleration of the head and for the shear force of the lower neck was slightly higher for the low loading rate as compared to the high loading rate. For the translation between head and sled this difference was even statistically significant. Thus, if the shape of the crash pulse is not known, solely the peak bending moment of the lower neck and the peak angular acceleration of the head seem to be suitable predictors for the neck injury risk but not the peak shear force of the lower neck, the peak linear acceleration of the head and the translation between head and thorax.     

Electric images of two low resistance objects in weakly electric fish

Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through their skin. In weakly electric fish, these currents arise from a self-generated field (the electric organ discharge), depending on the electrical properties of the surrounding medium. The electric image can be defined as the pattern of transepidermal voltage distributed over the receptive surface. To understand electrolocation it is necessary to know how electric image of objects are generated. In pulse mormyrids, the electric organ is localized at the tail, far from the receptors and fires a short biphasic pulse. Consequently, if all the elements in the environment are resistive, the stimulus at every point on the skin has the same waveform. Then, any measure of the amplitude (for example, the peak to peak amplitude) could be the unique parameter of the stimulus at any point of the skin. We have developed a model to calculate the image, corroborating that images are spread over the whole sensory surface and have an opposite center-surround, "Mexican-hat" shape. As a consequence, the images of different objects superimpose. We show theoretically and by simulation that the image of a pair of objects is not the simple addition of the individual images of these objects.     

Electromagnetic pulse propagation in dispersive planar dielectrics

The responses of a plane-wave pulse train irradiating a lossy dispersive dielectric half-space are investigated. The incident pulse train is expressed as a Fourier series with summing done by the inverse fast Fourier transform. The Fourier series technique is adopted to avoid the many difficulties often encountered in finding the inverse Fourier transform when transform analyses are used. Calculations are made for propagation in pure water, and typical waveforms inside the dielectric half-space are presented. Higher harmonics are strongly attenuated, resulting in a single continuous sinusoidal waveform at the frequency of the fundamental depth in the material. The time-averaged specific absorption rate (SAR) for pulse-train propagation is shown to be the sum of the time-averaged SARs of the individual harmonic components of the pulse train. For the same average power, calculated SARs reveal that pulse trains generally penetrate deeper than carrier-frequency continuous waves but not deeper than continuous waves at frequencies approaching the fundamental of the pulse train. The effects of rise time on the propagating pulse train in the dielectrics are shown and explained. Since most practical pulsed systems are very limited in bandwidth, no pronounced differences between their response and continuous wave (CW) response would be expected. Typical results for pulse-train propagation in arrays of dispersive planar dielectric slabs are presented. Expressing the pulse train as a Fourier series provides a practical way of interpreting the dispersion characteristics from the spectral point of view.     

Passive transmembrane redistributions of phospholipids as a determinant of erythrocyte shape change. Studies on electroporated cells

Echinocytes formed from discocytic erythrocytes by electric field pulses at 0 degrees C return to the discoytic shape upon incubation at 37 degrees C and subsequently turn into stomatocytes. Active and passive components of phospholipid translocation are involved in this shape recovery. Following low-field-strength pulses (5 kV cm-1), shape recovery is fully suppressed by ATPase inhibitors, such as vanadate. When vanadate is only added after stomatocyte formation has been completed, the cells return to the stage of echinocytosis prevailing before recovery. At higher field strength (7 kV cm-1) and in particular after repetitive field pulses, the subsequent incubation at 37 degrees C results in partial shape recovery even in the presence of vanadate. On the basis of the enhanced passive transmembrane mobilities of phospholipid probes observed previously following electroporation, the shape changes in the presence of vanadate are proposed to be due to a passive net movement of phospholipids from the outer to the inner membrane leaflet, as a consequence of the different mobilities of the various membrane phospholipids. Repetitive pulses at higher field strengths lead to a progressively more discocytic stationary shape during subsequent resealing. This phenomenon is explained by the progressively increased transbilayer mobility of the normally almost immobile phospholipid sphingomyelin and a consecutive progressive symmetrization of all membrane phospholipds.