Team:Lambert GA/Hardware
E L E C T R O P E N
OVERVIEW
One of the most important processes within synthetic biology involves the introduction of small molecules through cell membranes, with the most prevalent being bacterial transformations. This process is routinely conducted using chemical means where washing of cells with numerous chemical mixtures allows for the creation of pores in the membrane. Another method commonly utilized is known as electroporation, where high-voltage pulses are delivered to cells resulting in temporary pore formation allowing the small molecules to enter. Electroporation is often favored due to its increased transformation efficiencies, faster protocols, and less materials necessary in preparing the competent cells, however, a major inhibitory factor persists due to the need for electroporators. These devices cost thousands of dollars, require electricity, and are difficult to transport, preventing their incorporation in many labs across the world, in high schools, and in field biology. With inspiration from frugal science inventions such as the Foldscope and PaperFuge, we set out to develop an electroporator that address each of these obstacles. We present the ElectroPen™, a novel 20-cent electroporator built using the underlying principles of a common household lighter that weighs only 13g, can be fabricated using everyday materials, and requires no access to electricity.
Figure 1: Design landscape of the ElectroPen™ system. a Illustration and depiction of the ElectroPen™, consisting of a toggle, casing, and wire terminals. b Design of the cuvette for electroporation, consisting of a 1.0mm gap in between two electrodes. c Origin of the piezoelectric mechanism found within the ElectroPen™. d Comparison of an industrial electroporator and the ElectroPen™.
ELECTROPORATION THEORY AND DESIGN PRINCIPLES
In order to demonstrate the versatility of electroporators, the underlying mechanism allowing their functioning must first be described. Cell membranes comprise of a combination of proteins, lipids, carbohydrates, and other macromolecule-based structures arranged into a bilayer formation providing a selectively permeable barrier to protect the cell and facilitate the transport of molecules into and out of the cell, thereby reducing the potential for molecules to freely diffuse into a cell [1]. This theory of the organization of the cell membrane in the formation of a phospholipid bilayer was characterized by Singer and Nicholson and named the “fluid mosaic model”, and the mosaic properties were further characterized as dominant to the fluidic properties [2]. Electroporation results in a disruption of membrane integrity [3-5], and the subsequent events following electrical discharge allow for membrane permeabilization [5-12]. While the actual molecular occurrences caused by electroporation that allow for DNA uptake are relatively unknown, experimental trials have indicated that interaction between the electrical fields and phospholipids result in the creation of aqueous pores in the membrane [13-15], high-voltage pulses stimulate a reorganization in the ions resulting in a new transmembrane voltage producing a local electrical field. These local electrical fields are theorized to lead to the formation of the aforementioned aqueous pores, allowing for the transport of molecules into a cell [16]. The totality of these sequence of events contribute to the uptake of DNA by cells in the processes of bacterial electrotransformations, but additionally function in cellular uptake for the other outlined applications of electroporation.
The observation of the effects of electrical pulses on living organisms can be traced back to the late 1700s when German physicist Georg Christoph Lichtenberg described branched structures that form when high-voltage electrical pulses are induced on human skin, which are now referred to as Lichtenberg Figures [17]. Over 200 years later, it was demonstrated that high-voltage pulses greatly increased the number of transfected cells, leading to the coinage of the term “electroporation”, based on the theory that these pulses induced temporary membrane disruptions allowing for DNA uptake [18]. Over the past decade, electroporation has been increasingly characterized in terms of its electrical and biological functionality, with elements such as field strength, voltage output, arc length, transformation efficiency, etc., leading to more advanced technology utilized to carry out the process. Additionally, an increase in the theoretical understanding behind electroporation’s principles has expanded its applications tremendously, including for cancer therapies through electrochemotherapy and electrically-induced tumor apoptosis, transdermal drug delivery, vaccine delivery, etc [19-22]. This versatility in terms of functionality and applicability for the electroporator indicates its importance in biotechnology and medical fields, and with the inhibitory factors mentioned above limiting its incorporation into labs, schools, and even in field biology, the need for a low-cost portable electroporator has risen greatly.
In contrast with the existing bulky and complex electroporators available commercially, the ElectroPen™ stems from a basic design incorporating readily available components, including a conventional household stove lighter. It is actuated using a toggle which pushes down the hammer action controlling the force generation on the piezoelectric crystal. The user exerted force allows for the hammer action to proceed through several phases (described below), allowing for discharge of the high-voltage pulse. The casing additionally allows for the attachment of copper wires to those already existing on the crystal, and heat-sensitive insulation is coated on the copper wire to prevent the user from experiencing any electrical shock. The ElectroPen™ thereby requires no access to electricity, can be fabricated in approximately 15 minutes, is portable, and costs only 23 cents to build (Cost per unit per 10,000 units excluding production costs).
Although standard electroporation cuvettes provided by companies have been shown to function optimally in electroporation, these cuvettes were found to not operate with the same conditions with the ElectroPen™. Additionally, these standard cuvettes are relatively expensive and difficult to produce without industrial equipment. Recognizing the perceived limitations of this cuvette, we developed a custom cuvette that can be built using a wide range of materials (glass slides, wood, etc.). The design of these cuvettes models its industrial equivalents, wherein two metal plates functioning as electrodes create an arc gap in a case. In our fabricated cuvettes, two large pieces of a specific material are covered with aluminum foil and sealed to a base, with a gap created in between each piece to serve as the arc gap for electroporation. The simplicity of the overall ElectroPen™ and cuvette model demonstrates the application of simple tools found everywhere across the world for a unique purpose at a fraction of the cost, hence acting as a major catalyst in the development of new similar tools which don’t have the same constraints as their commercial versions.
Since the conception of electroporation, numerous systems and machines have been developed to carry out successful and efficient electroporation, in recognition of the various parameters that must be optimized [23-25], including field strength, voltage, pulse length, number of pulses, temperature, pH, ion concentration, phase of growth for harvested cells, cell density, etc. [26-27]. With respect to bacteria, the most common method involves capacitance discharge in the form of an exponentially decaying wave for electrotransformations [28-29]. The prevalence of this model is due to the simplicity of its design, with the simplest circuits including a high-voltage power supply (V), switch (S), a capacitor (C) , and often a resistor (R) for modulation of voltage outputs. It functions in two phases: a charge phase and a discharge phase, in which the former includes the power supply charging the capacitor with the switch in one position, and the latter with the switch in a different position allowing the capacitor to discharge through the load (solution) connected as an output in the circuit. The other common method utilized for electroporation includes the generation of square wave pulses, consisting of significantly shorter fall times than the exponential decay model. Square wave pulses are primarily used for electroporation of eukaryotic cells, although they have been demonstrated to successfully (and optimally) electrotransform [30]. Within the ElectroPen™, the piezoelectric element described below generates exponentially decaying pulses with voltage outputs and time constants similar to the 1800V/5ms values optimized for E. coli, however, the generated pulse does not involve any of the previously described circuitry, using a piezoelectric mechanism for generation and release of the voltage rather than a traditional power supply, allowing for no necessity for access to electricity to operate the device.
The crystal found within the ElectroPen™ is composed of lead zirconate titanate (PZT), a particularly sensitive material known to produce high voltages even with a slight deformation of the crystal [31]. Using an oscilloscope, the voltage outputs and time constants for several different strikes of the PZT crystal from the lighter were quantified and demonstrated to have significant consistency, with the average peak output at 1997.8378 V (S.D. 278.2399 V). The time constant has been shown to have slight variation, with the average time constant at 5.1362 ms (S.D. 0.8927 ms), with trials conducted by 3 individuals across the ages of 18-25, with most values within the necessary range for successful electroporation. Through this, we’ve experimentally determined that the ElectroPen™ is capable of successfully producing high-voltage pulses within the optimal ranges for electroporation of E. coli, however, to understand how this occurs, the underlying mechanisms for voltage generation must be described. Therefore, we developed a theoretical model to characterize the functionality of the ElectroPen™.
The observation of the effects of electrical pulses on living organisms can be traced back to the late 1700s when German physicist Georg Christoph Lichtenberg described branched structures that form when high-voltage electrical pulses are induced on human skin, which are now referred to as Lichtenberg Figures [17]. Over 200 years later, it was demonstrated that high-voltage pulses greatly increased the number of transfected cells, leading to the coinage of the term “electroporation”, based on the theory that these pulses induced temporary membrane disruptions allowing for DNA uptake [18]. Over the past decade, electroporation has been increasingly characterized in terms of its electrical and biological functionality, with elements such as field strength, voltage output, arc length, transformation efficiency, etc., leading to more advanced technology utilized to carry out the process. Additionally, an increase in the theoretical understanding behind electroporation’s principles has expanded its applications tremendously, including for cancer therapies through electrochemotherapy and electrically-induced tumor apoptosis, transdermal drug delivery, vaccine delivery, etc [19-22]. This versatility in terms of functionality and applicability for the electroporator indicates its importance in biotechnology and medical fields, and with the inhibitory factors mentioned above limiting its incorporation into labs, schools, and even in field biology, the need for a low-cost portable electroporator has risen greatly.
In contrast with the existing bulky and complex electroporators available commercially, the ElectroPen™ stems from a basic design incorporating readily available components, including a conventional household stove lighter. It is actuated using a toggle which pushes down the hammer action controlling the force generation on the piezoelectric crystal. The user exerted force allows for the hammer action to proceed through several phases (described below), allowing for discharge of the high-voltage pulse. The casing additionally allows for the attachment of copper wires to those already existing on the crystal, and heat-sensitive insulation is coated on the copper wire to prevent the user from experiencing any electrical shock. The ElectroPen™ thereby requires no access to electricity, can be fabricated in approximately 15 minutes, is portable, and costs only 23 cents to build (Cost per unit per 10,000 units excluding production costs).
Although standard electroporation cuvettes provided by companies have been shown to function optimally in electroporation, these cuvettes were found to not operate with the same conditions with the ElectroPen™. Additionally, these standard cuvettes are relatively expensive and difficult to produce without industrial equipment. Recognizing the perceived limitations of this cuvette, we developed a custom cuvette that can be built using a wide range of materials (glass slides, wood, etc.). The design of these cuvettes models its industrial equivalents, wherein two metal plates functioning as electrodes create an arc gap in a case. In our fabricated cuvettes, two large pieces of a specific material are covered with aluminum foil and sealed to a base, with a gap created in between each piece to serve as the arc gap for electroporation. The simplicity of the overall ElectroPen™ and cuvette model demonstrates the application of simple tools found everywhere across the world for a unique purpose at a fraction of the cost, hence acting as a major catalyst in the development of new similar tools which don’t have the same constraints as their commercial versions.
Since the conception of electroporation, numerous systems and machines have been developed to carry out successful and efficient electroporation, in recognition of the various parameters that must be optimized [23-25], including field strength, voltage, pulse length, number of pulses, temperature, pH, ion concentration, phase of growth for harvested cells, cell density, etc. [26-27]. With respect to bacteria, the most common method involves capacitance discharge in the form of an exponentially decaying wave for electrotransformations [28-29]. The prevalence of this model is due to the simplicity of its design, with the simplest circuits including a high-voltage power supply (V), switch (S), a capacitor (C) , and often a resistor (R) for modulation of voltage outputs. It functions in two phases: a charge phase and a discharge phase, in which the former includes the power supply charging the capacitor with the switch in one position, and the latter with the switch in a different position allowing the capacitor to discharge through the load (solution) connected as an output in the circuit. The other common method utilized for electroporation includes the generation of square wave pulses, consisting of significantly shorter fall times than the exponential decay model. Square wave pulses are primarily used for electroporation of eukaryotic cells, although they have been demonstrated to successfully (and optimally) electrotransform [30]. Within the ElectroPen™, the piezoelectric element described below generates exponentially decaying pulses with voltage outputs and time constants similar to the 1800V/5ms values optimized for E. coli, however, the generated pulse does not involve any of the previously described circuitry, using a piezoelectric mechanism for generation and release of the voltage rather than a traditional power supply, allowing for no necessity for access to electricity to operate the device.
Figure 2: Exponentially decaying model of the ElectroPen™. Waveform illustrates the pulse delivered by the ElectroPen™, achieving a signal aligned peak of 1.834kV and 5.16ms time constant.
The crystal found within the ElectroPen™ is composed of lead zirconate titanate (PZT), a particularly sensitive material known to produce high voltages even with a slight deformation of the crystal [31]. Using an oscilloscope, the voltage outputs and time constants for several different strikes of the PZT crystal from the lighter were quantified and demonstrated to have significant consistency, with the average peak output at 1997.8378 V (S.D. 278.2399 V). The time constant has been shown to have slight variation, with the average time constant at 5.1362 ms (S.D. 0.8927 ms), with trials conducted by 3 individuals across the ages of 18-25, with most values within the necessary range for successful electroporation. Through this, we’ve experimentally determined that the ElectroPen™ is capable of successfully producing high-voltage pulses within the optimal ranges for electroporation of E. coli, however, to understand how this occurs, the underlying mechanisms for voltage generation must be described. Therefore, we developed a theoretical model to characterize the functionality of the ElectroPen™.
Figure 3: Voltage/time constant model for the ElectroPen™. a Time constant is defined as the time taken to achieve 1/3rd of the peak voltage. b Comparison of voltage/time constant outputs of the ElectroPen™ to those optimized for electroporation of E. coli. The majority of those produced by the ElectroPen™ fall within the expected range, demonstrating its functionality.
THEORETICAL MODEL AND EVALUATION
Voltage outputs from any piezoelectric-based system are dependent on the force exerted on the crystal, allowing for the reorganization of the ions, creating the corresponding output [32]. In order to characterize the capability of a small lighter to generate high voltages (on the order of kilovolts), the underlying mechanism within the lighter must first be described. The mechanism (which will henceforth be referred to as the “hammer action”) comprises of two springs, a hammer (metal piece striking the crystal), and the PZT crystal itself connected to a metal conductor. The hammer action functions in three phases: a loading phase, a release phase, and a relaxation phase, each directed by various components. During the loading phase, the hammer is held in a locked position as the lower spring and upper springs are being compressed using the user exerted force. The entire upper portion of the casing moves upwards, while the hammer is still locked in a loading position. The time interval of the loading phase is dependent on the force exerted by the user, and has no effect on the output voltage as the hammer's movement is dependent on the spring release. At the release phase, once the action begins to approach is critical point, the lower casing with a connected wedge pushes the hammer out of the latch while the spring is compressed at maximum, beginning to release the hammer. Then, the hammer switches from the lock to unlock state, allowing the lower spring to extend and project the hammer towards and onto the piezoelectric crystal, with the upper spring remaining compressed. The relaxation phase then constitutes the user pulling back, extending the upper spring, forcing the hammer downwards into its original state with no effect on the lower spring. Analysis of high-speed videos of the hammer releasing indicate that the hammer is able to reach a maximum velocity of 8 m/s at a peak acceleration of 30,000 m/s2. Further analysis indicates this rapid acceleration produces jerk of up to 300,000,000 m/s3 from this small hammer action, indicating the extreme nature of the design, allowing for the production of a powerful resultant force striking the crystal. In an effort to characterize the correlation between the experimentally obtained voltage outputs using the ElectroPen™ and the theoretical outputs, a piezoelectric static voltage theoretical model was used. Through this model and the data values established as constants , the theoretical voltage output of the crystal found within the lighter is a maximum of 2699 Volts, with a lower output under normal conditions due to the strain on the crystal from expanding towards its maximum length, as well as the resistance caused by the copper wires and metal conductors in the lighter. As the values from the described lighter are of the same magnitude, it can be declared that the theoretical basis confirms the obtained values from the experimental trials.
After conducting electroporation trials with the described protocol (Refer to Protocols below), growth of colonies as well as GFP expression were subsequently analyzed. Plates with growth were isolated and inoculated into liquid cultures, and quantified using the plate reader . GFP expression levels were thereby analyzed with a comparison of the ElectroPen™ to the outputs from an industrial electroporator (BioRad MicroPulser). With the negative control serving as the baseline comparison for validating positive expression of GFP, it can clearly be seen that there is a significant difference in fluorescence intensity (represented as Fluorescence/OD600) between the negative and positive control, confirming that GFP was successfully electroporated. The experimental samples were conducted using the ElectroPen™ and the positive control with the BioRad electroporator. It can be seen that the fluorescence intensity values for the ElectroPen™ trials are similar to the outputs produced by the standard electroporator, indicating successful electroporation, uptake of DNA, and expression of GFP by the E. coli bacteria. The obtained transformation efficiency (similar to the BioRad Micropulser) from the experimental trial additionally indicates the functionality of the ElectroPen™, presenting it as a powerful device for infield and low-resource settings.
Figure 4: Mechanical model of the ElectroPen™. a Depiction of the piezoelectric ignition found within a conventional lighter. b Parts of the mechanism, including from top to bottom: metal conductor housing crystal, loading/relaxation phase springs, hammer, release phase spring, and applied force casing. c Image trace of the hammer action throughout the three phases. The point of focus (marked in red) is the hammer arm. d Position graph of the hammer arm in comparison with the applied force casing through the three separate phases. e-g Motion of hammer during the release phase. e Displacement of hammer arm during release phase. f Velocity of the hammer during the release phase, reaching a peak of 8m/s. g Acceleration of the hammer during the release phase, reaching a peak of 30,000 m/s2 producing a corresponding force of 10N.
Figure 5: Derived mathematical model for calculating theoretical maximum voltage for the ElectroPen™. Using previously described models, a final model was obtained incorporating dimensions and the disc-orientation of the ElectroPen™, resulting in an amplified voltage output. Using established parameters for piezoelectric constants, we arrived at a theoretical maximum of 2.699kV, with the resistance in our system due to strain constraints and wire resistance.
After conducting electroporation trials with the described protocol (Refer to Protocols below), growth of colonies as well as GFP expression were subsequently analyzed. Plates with growth were isolated and inoculated into liquid cultures, and quantified using the plate reader . GFP expression levels were thereby analyzed with a comparison of the ElectroPen™ to the outputs from an industrial electroporator (BioRad MicroPulser). With the negative control serving as the baseline comparison for validating positive expression of GFP, it can clearly be seen that there is a significant difference in fluorescence intensity (represented as Fluorescence/OD600) between the negative and positive control, confirming that GFP was successfully electroporated. The experimental samples were conducted using the ElectroPen™ and the positive control with the BioRad electroporator. It can be seen that the fluorescence intensity values for the ElectroPen™ trials are similar to the outputs produced by the standard electroporator, indicating successful electroporation, uptake of DNA, and expression of GFP by the E. coli bacteria. The obtained transformation efficiency (similar to the BioRad Micropulser) from the experimental trial additionally indicates the functionality of the ElectroPen™, presenting it as a powerful device for infield and low-resource settings.
Figure 6: a Fluorescence expression from the trials conducted with the electroporator and ElectroPen™. As can be seen, GFP expression from the ElectroPen™ is comparable to the electroporator (BioRad Micropulser), indicating successful transformation and uptake of DNA. b-c Efficiency of the trials. It can be seen that the ElectroPen™ has similar transformation efficiencies as the electroporator, demonstrating its functionality.
PRODUCT DESIGN AND GLOBAL COLLABORATION
A key component of demonstrating the accuracy and precision of scientific data is through reproducibility and external validation. We believe that collaboration with other iGEM teams is a powerful method to disseminate information, and in this spirit, we have worked with the University of Georgia iGEM Team and Taiwanese American School iGEM Team to verify the functionality and practicality of our device. Throughout multiple trials conducted by both teams, the ElectroPen™ was demonstrated to successfully electroporate GFP into E. coli, as seen with the trials conducted by Lambert iGEM. The transformation efficiency obtained from these tests is also on par with those from commercial electroporators, thereby confirming the data obtained across all trials conducted. Through this, we demonstrate that the ElectroPen™ (patent pending) is a powerful ultralow-cost device that can be applied in various settings from low-resource high school groups to equipped university laboratories, and we envision the application of this device in these settings across the world.
In order to ensure effective implementation of this device across the world, we have received feedback and design inputs for improvements and suggestions for the ElectroPen. From both the TAS Taipei and UGA teams, we received suggestions to increase the length of the wires and create terminals on the cuvettes such that the ElectroPen can connect to it. We also received recommendations to create a latch for the toggle to remain secured within the casing. In recognition of these suggestions, we will soon develop another iteration of the ElectroPen as an improvement.
We recognize the importance of collaboration in the validation of the ElectroPen's functionality, and in next year's project, will conduct a larger international collaboration study with the ElectroPen to further demonstrate reproducibility and the versatility.
The tutorials and instructions to build the ElectroPen system have not yet been released as an open-access publication comprising of these documents will soon be released. However, all interested teams may visit our booth during the exhibition session at Jamboree to register to participate in a mini-InterLab Study for the ElectroPen with supplies provided by us!
In order to ensure effective implementation of this device across the world, we have received feedback and design inputs for improvements and suggestions for the ElectroPen. From both the TAS Taipei and UGA teams, we received suggestions to increase the length of the wires and create terminals on the cuvettes such that the ElectroPen can connect to it. We also received recommendations to create a latch for the toggle to remain secured within the casing. In recognition of these suggestions, we will soon develop another iteration of the ElectroPen as an improvement.
We recognize the importance of collaboration in the validation of the ElectroPen's functionality, and in next year's project, will conduct a larger international collaboration study with the ElectroPen to further demonstrate reproducibility and the versatility.
The tutorials and instructions to build the ElectroPen system have not yet been released as an open-access publication comprising of these documents will soon be released. However, all interested teams may visit our booth during the exhibition session at Jamboree to register to participate in a mini-InterLab Study for the ElectroPen with supplies provided by us!
Figure 7: a We worked with TAS_Taipei to validate the ElectroPen™’s efficacy, and through two trials conducted, they successfully demonstrated that electroporation using the device was successful. b Collaboration with the University of Georgia team on 3 different trials also indicated the same results, validating the performance of the ElectroPen™.
REFERENCES
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[28]Neumann, E. & Rosenheck, K. Permeability changes induced by electric impulses in vesicular membranes. The J. Membr. Biol. 10, 279–290, DOI: 10.1007/BF01867861 (1972).
[29]Takahashi, M. et al. Gene transfer into human leukemia cell lines by electroporation: Experience with exponentially decaying and square wave pulse. Leuk. Res. DOI: 10.1016/0145-2126(91)90062-X (1991).
[30]Eynard, N., Rodriguez, F., Trotard, J. & Teissié, J. Electrooptics studies of Escherichia coli electropulsation: Orientation, permeabilization, and gene transfer. Biophys. J. DOI: 10.1016/S0006-3495(98)77704-5 (1998).
[31]Shkuratov, S. I. et al. Compact high-voltage generator of primary power based on shock wave depolarization of lead zirconate titanate piezoelectric ceramics. Rev. Sci. Instruments DOI: 10.1063/1.1771490 (2004).
[32]Butt,Z.&Pasha,R.A.Effectoftemperatureandloadingonoutputvoltageofleadzirconatetitanate(PZT-5A)piezoelectric energy harvester. In IOP Conference Series: Materials Science and Engineering, DOI: 10.1088/1757-899X/146/1/012016(2016).
[2]Engelman, D. M. Membranes are more mosaic than fluid. Nature 438, 578–580, DOI: 10.1038/nature04394 (2005).
[3]Neumann, E., Sowers, A. E. & Jordan, C. A. (eds.) Electroporation and Electrofusion in Cell Biology (Springer US, Boston, MA, 1989).
[4]Nickoloff, J. A. Animal Cell Electroporation and Electrofusion Protocols, vol. 48 (Humana Press, New Jersey, 1995).
[5]Glaser, R. W., Leikin, S. L., Chernomordik, L. V., Pastushenko, V. F. & Sokirko, A. I. Reversible electrical breakdown of lipid bilayers: formation and evolution of pores. BBA - Biomembr. 940, 275–287, DOI: 10.1016/0005-2736(88)90202-7(1988).
[6]Needham, D. & Hochmuth, R. M. Electro-mechanical permeabilization of lipid vesicles. Role of membrane tension and compressibility. Biophys. J. 55, 1001–1009, DOI: 10.1016/S0006-3495(89)82898-X (1989).
[7]Neumann, E. & Rosenheck, K. Permeability changes induced by electric impulses in vesicular membranes. The J. Membr. Biol. 10, 279–290, DOI: 10.1007/BF01867861 (1972).
[8]Teissié, J., Eynard, N., Gabriel, B. & Rols, M. P. Electropermeabilization of cell membranes. Adv. Drug Deliv. Rev. 35, 3–19, DOI: 10.1016/S0169-409X(98)00060-X (1999).
[9]Yow Tsong, T. [25] Electric modification of membrane permeability for drug loading into living cells. 248–259, DOI:10.1016/0076-6879(87)49063-0 (1987).
[10]Weaver, J. C. Electroporation Theory: Concepts and Mechanisms. In Electroporation Protocols for Microorganisms, 1–26, DOI: 10.1385/0-89603-310-4:1 (Humana Press, New Jersey).
[11]Zimmermann, U., Pilwat, G., Beckers, F. & Riemann, F. Effects of external electrical fields on cell membranes. Bioelectro- chemistry Bioenerg. 3, 58–83, DOI: 10.1016/0302-4598(76)85007-6 (1976).
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