COMMUNICATION TO THE EDITOR

Variable Electric Fields for High ThroughputElectroporation Protocol Design inCurvilinear Coordinates

Francois Fernand, Liel Rubinsky, Alex Golberg, Boris Rubinsky

Department of Mechanical Engineering, Etcheverry Hall, 6124, University of California at

Berkeley, 2521 Hearst Ave, Berkeley, California 94720; telephoneQ2: XXX; fax: XXX;

e-mail: alex.golberg@berkeley.edu

Received 14 October 2011; revision received 5 January 2012; accepted 9 February 2012

Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/bit.2447

9

ABSTRACT: The mathematical solution to the electric fieldequation in cylindrical coordinates, has suggested to us anew experimental methodology and device for reducingexperimental effort in designing electroporation protocols.Using a new cylindrical electroporation system, we show,with an Escherichia coli cell model, how key electroporationparameters emerge precisely from single experiments ratherthan through interpolation from numerous experiments inthe conventional Cartesian electroporation system.

Biotechnol. Bioeng. 2012;9999: 1–6.

� 2012 Wiley Periodicals, Inc.

KEYWORDS: high throughput; electroporation; protocoldesign

The permeabilization of the cell membrane using electricfields applied across the membrane is known as electropo-ration (Neumann et al., 1982) or electropermeabilization(Stopper et al., 1985). Electroporation is reversible whencells survive the electropermeabilization and irreversiblewhen they do not. Reversible electroporation is commonlyused in biotechnology and medicine for such applications asgene or drug delivery into cells (Dev et al., 2000). Irreversibleelectroporation is important for non-thermal sterilization inthe food industry, biotechnology and medicine, and fortissue ablation in medicine (Pakhomov et al., 2010;Rubinsky, 2010).

The outcome of an electroporation protocol, whetherreversible or irreversible, depends on the parameters of theelectric field such as strength, pulse length, number ofpulses, time interval between pulses, frequency; on solutioncomposition, pH, temperature and on cell type, shape andsize. Because electroporation depends on so many param-eters, designing optimal electroporation protocols requirestedious and lengthy efforts. To illustrate the complexity of

Correspondence to: A. Golberg

� 2012 Wiley Periodicals, Inc.

BIT-11-9

protocol design, Figure 1 shows a theoretical curve adaptedfrom (Dev et al., 2000), which correlates electric fieldstrength, single pulse length and the biophysical phenome-non that occurs when the particular parameters are appliedacross a cell. One of themost important features of the figureis the line that separates between the reversible andirreversible electroporation domains, which is critical indesigning optimal electroporation protocols. In optimalreversible electroporation it is desirable to be close to andbelow that line while in optimal irreversible electroporationit is desirable to be close to and above that line.Conventional methods for the systematic development ofoptimal electroporation protocols employ experimentalsystemsmade of two parallel electrodes, bounding the mediaof interest, in a one-dimensional Cartesian configuration(e.g., Sale and Hamilton, 1967; Hamilton and Sale, 1967).The solution to the simple Laplace equation (r2’ ¼ 0;where w is the potential) for a homogeneous Cartesiansystem, subject to constant voltage boundary conditions onthe electrodes, V2 and V1, gives an expression for the electricfield between the planar electrodes. It is, ðV2 � V1Þ=L whereL is the distance between the electrodes. It is evident that theCartesian configuration produces a constant electric field inthe treated medium between the electrodes. Identifying theelectric field parameters that separate between reversible andirreversible electroporation requires numerous constantelectric field experiments, in which the electric field strengthis continuously changed in separate experiments until theinterface is detected approximately, through interpolationbetween experiments (Rubinsky et al., 2008).

Several approaches were introduced for multiparameteroptimization of in vitro and in vivo electroporation. Heiser(1999) published an extensive review on electroporationparameters for various cell lines and general guidelines forelectroporation protocol optimizations in vitro (Heiser,1999). A review and guidelines for optimization of in vivoelectroporation applications was reported by Gehl (2003).

Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2012 1

43.R1(24479)

Figure 1. Theoretical mapping of biophysical effects experienced by cells as a

function of electroporation parameters.

Figure 2. Electroporation parameters analysis: (a) image of a plate electro-

porated in one-dimensional cylindrical coordinates, after incubation. The central part

has no cell colonies, (b) a schematic view of the analyzed cylindrical system. Two

cylindrical electrodes with radiuses R1 and R2 were used. The radius (r) of irreversible

electroporated zone was measured. c: Calculated electric field-radius (r) correlation

for the experiment, (d) electric parameters that identify the conditions in which

irreversible electroporation occurs during electroporation of E. coli in pH buffered

medium (error bar 1 standard deviation).

Furthermore, several statistical methodologies were pro-posed to reduce the number of experiments required forprotocol optimizations. Multifactorial experimental designfor optimizing transformation protocols was introduced by(Marciset and Mollet, 1994). Keng-Shiang et al. (2007) usedthe Taguchi Method for the optimization of gene electro-transfer (Keng-Shiang et al., 2007). Recently, a centralcomposite design was used to optimize electroporationprotocols (Madeira et al., 2010).

In this study we developed a different approach tomultiparameter optimization, based on the use in a singleexperiment of a well-defined variable electric field topologyin the curvilinear coordinate system. The concept will beillustrated with a simple to implement cylindrical coordinatesystem. The electric field calculated from the solution to theone-dimensional Laplace equation in cylindrical coordi-nates, in a medium between two cylinders of radiuses R1 andR2 on which electric potentials of V1 and V2 are imposed,respectively, is given by,

V1 � V2

r � ln R2

R1

� �

where r is the variable radius inside the domain of interest.Obviously, the electric field varies continuously as an inversefunction of the radius. (In one-dimensional sphericalcoordinates the electric field varies as one over the radiussquared.) Therefore, in a single experiment in one-dimensional cylindrical or spherical electrode systems, thecells between the electrodes will experience a continuouslyvariable electric field, that is, nevertheless, well defined as afunction of the radius. The response of the cells to anyelectroporation protocol can be evaluated as a function oftheir relative location (defined by radius) and therebycorrelated to the electric field. Therefore, when an

2 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2012

experiment is performed with cylindrical (or spherical)electrodes, the results of a single experiment producecontinuous information on the effect of a wide range ofelectric fields, which are quantified by the radius at whichthey are produced. In contrast, to produce similarinformation, the conventional Cartesian electrode systemrequires a very large number of experiments and theinterpolation of results between the studied discrete datapoints.

Figure 2 illustrates results obtained from a studyperformed with a one-dimensional cylindrical system, usingEscherichia coli BL21 (D13) PSJS1244, an ampicillin stablestrain. The Figure 2d shows the electric field at the reversible/irreversible interface as a function of the number of pulses.The microorganisms were spread on a Petri dish and aconstant pulsed electric potential was imposed on twoconcentric metal cylinders, in contact with the surface onwhich the microorganism was plated. In the one-dimen-sional cylindrical electrode system used, the outer diameterof the inner cylinder was 1.18mm and the inner diameter ofthe outer cylinder was 22.15mm. The electric pulse wasdelivered by a BTX (BTX ECM 830, Harvard Apparatus,MAQ3). Four sites were treated in each Petri dish, after whichthe samples were incubated for 18 h at 378C and examined.Figure 2a and d reports on results with a pH buffered plate,at which pH did not change after the application of electricfield, and in which 2,200 V pulses were applied between theconcentric electrodes in 40ms pulse duration at 1Hzfrequency. Five repeats were performed for each condition.

It should be emphasized that each data point on the curveswas obtained from a single experiment (with five repeats). Incontrast, obtaining such a single data point with Cartesianelectrodes would require numerous single electric fieldexperiments and interpolation.

Figure 2b and c shows how the plot in Figure 2d wasobtained. Figure 2a shows the appearance of a treatedcylinder after incubation. It is evident that the cells in thecentral area did not survive the electric fields to which theywere exposed and did not form colonies. To determine theradius of cell death we measured the innermost radius of thecolonies that survived electroporation, as described in theMaterials and Methods Section. Figure 2b shows the modelof the analyzed system. Two cylindrical electrodes, withradiuses of R1 and R2, and a measured radius (r) of a zonewhere irreversible electroporation takes place, are shown onFigure 2b. Then, the mathematical expression for the electricfield as a function of radius in cylindrical coordinates wasused to produce Figure 2c. Figure 2c is used to correlate theradius of cell death in Figure 2a with the electric field at thatradius. The electric field at the radius of cell death is thanplotted as a function of number of pulses in Figure 2d. Thisplots the electric parameters at which irreversible electro-poration begins.

In summary, we propose that the use of cylindrical one-dimensional electrodes will substantially reduce the numberof experiments needed to design optimal electroporationprotocols, over those obtained with the use of traditionalCartesian electrodes. In this report we have shown the use ofthe concept for obtaining the reversible/irreversible inter-face. Obviously a similar experiment with fluorescence diesor genes can be used to determine the parameters at theinterface between reversible and no effect electric fields.Furthermore, this method provides a means to examine in asingle experiment, various colonies that have undergoneelectroporation with a wide range of well-defined electro-poration parameters. The relative location of each colony ofinterest identifies the electroporation conditions it hasexperienced. It should be noted that the idea of a well-defined topological space of variable electric fields could beextended through further research in topology to the designof systems of more complex surfaces than the cylinder orsphere, which may produce in a single experiment complexranges of parameters of interest.

Materials and Methods

Experimental Device

The cylindrical one-dimensional electroporation electrodeswere manufactured using a Perspex ‘‘square’’ (3 cm by 3 cm)basis. A half cm notch carved in the side of the square wasattached to the top of a brass ring using a heated glue gun.The brass ring had an inside diameter of 22.15mm, anoutside diameter of 25.40mm, and a height of 4mm. The tipof an 18 gauge steel needle (Precision Glide needle, Becton

Dickinson & Co, NJQ4) was cut 1 cm from the top, to formthe inner, 0.6mm radius cylinder. The needle was theninserted through the center of the plastic square in themiddle of the brass ring forming two concentric cylinders.

Electroporation Procedure

The study was performed using E. coli BL21 (D13) PSJS1244an ampicillin stable strain. A single E. coli colony was used toinoculate 50mL of sterile LB Broth (Ditco, NYQ5)containing 100mg/mL of ampicillin (American SystemQ6).The sample was placed in a Thermo Scientific MaxQ 4450shaker-incubator. The temperature was maintained at 378C.The shaker speed was 200 rpm to allow aeration for optimalgrowth. The sample was kept in the shaker-incubator for14 h to reach stationary phase. The final concentration ofapproximately 106 CFU/mL was determined by viable countmethod. After 14 h in the shaker-incubator a 100mL samplewas removed and diluted in 10mL of sterile water (100�dilution) 100mL of the diluted sample was plated on to eachpre-prepared agar plate and spread using glass beads(Novagen, CAQ7). The glass beads were removed and theelectroporation device was inserted into the agar in onequadrant of the Petri dish. The device was pushed into theagar plate until the ring and needle touched the Petri dishbottom in order to ensure they were at the same depth.Alligator clips were attached to the brass ring and the 18Gneedle. The alligator clips were never in direct contact withthe agar to ensure no direct discharge into the gel. Thisallowed the field to be equally distributed around the needle.The clips were hooked up to the BTX (BTX-model 610, BTXECM 830 square-wave electroporator, Harvard Apparatus).The electroporation parameters used were 2,200 V, 40mspulse duration, 1Hz frequency. The numbers of pulses werechanged between experiments. Statistical analysis was donewith the final parameters recorded from the BTX device.

Following the electroporation the needle and the ringwere removed from the agar gel. (A similar experiment wasthan performed in another quadrant. A total of fourexperiments were performed per dish.) A total of fiveexperiments per parameter were performed. After theexperiment the Petri dish was incubated at 378C for 18 h.Following the incubation period the dishes were removedand IRE curve radius was measured.

Plate Preparation

Agar Petri plates were prepared to maintain pH 7 after theapplication of electric pulses. The mixture was composed of0.1 g/L NaCl (Spectrum Chemical, Mfg Corp, CAQ8), 10 g/LBactotryptone, 5 g/L Yeast Extract, 15 g/L Bacto Agar(Becton Dickinson & Co, NJQ9), 0.5 g/L glucose wasdissolved in distilled water and heated at 1218C in anautoclave for 15min. After cooling down and reaching 508C,23.83 g/L HEPES (Sigma-Aldrich, CQ10A) and ampicillin(American BioanalyticalQ11) at 10mg/mL was added to

Fernand et al.: VariableQ1 Electric Fields 3

Biotechnology and Bioengineering

100mg/mL final concentration. The buffered agar was thenpoured into a 100mm Petri dish and the drying timebetween the pouring and the closing of the plates was6.5min. In fact, the evaporation of water during storagemust be taken into account because it changes the NaClconcentration and of course the conductivity of themedium.

Radius Measurement and Statistical Analysis

Electroporated plates were removed from the incubator after18 h. Digital images of the plates and scale reference weretaken and then used to determine the death zone diameter.The error on the electric field estimate includes the diametermeasurement errors (precision of 0.05mm) and the BTXdevice output error (20 V). The reported radius is an averageof five repeats with a standard deviation calculated from thefive measurements.

References

Dev S, Rabussay D, Widera D, Hofmann G. 2000. Medical applications of

electroporation. IEEE Trans Plasma Sci 28(1):206–223.

Gehl J. 2003. Electroporation: Theory and methods, perspectives for drug

delivery, gene therapy and research. Acta Physiol Scand 177(4):

437–447.

4 Biotechnology and Bioengineering, Vol. 9999, No. 9999, 2012

Hamilton WA, Sale AJH. 1967. Effect of high electric field on micro-

organisms. II. Mechanism of action of the lethal effect. Biochim

Biophys Acta 148:788–800.

Heiser WC. 1999. Optimizing electroporation conditions for the transfor-

mation of mammalian cells. In: Tymms MJ, editor. Transcription

factor protocols. Totowa, New Jersey: Springer. p 117–134.

Keng-Shiang H, Sheng-Chung Y, Hung-Yi C, Yu-Cheng L. 2007. Optimi-

zation of Gene Transfection Condition using Taguchi Method for an

Electroporation Microchip; June 10–14, 2007. p 847–850.

Madeira C, Ribeiro S, TurkM, Cabral J. 2010. Optimization of gene delivery

to HEK293T cells by microporation using a central composite design

methodology. Biotechnol Lett 32(10):1393–1399.

Marciset O, Mollet B. 1994. Multifactorial experimental design for

optimizing transformation: Electroporation of Streptococcus thermo-

philus. Biotechnol Bioeng 43(6):490–496.

Neumann E, Schaefer-Ridder M, Wang Y, Hofschneider PH. 1982. Gene

transfer into mouse lyoma cells by electroporation in high electric

fields. EMBO J 1(7):841–845.

Pakhomov AG, Miklavcic D, Markov MM. 2010. Advanced electroporation

techniques in biology and medicine. Boca Raton: CRC Press. 521 p.

Rubinsky B, editor. ‘‘Irreversible Electroporation’’ Springer. Series in

Biomedical Engineering 2010, XIV, 314 p. Hardcover Chennai ISBN:

978-3-642-05419-8.

Rubinsky J, Onik G,Mikus P, Rubinsky B. 2008. Optimal parameters for the

destruction of prostate cancer using irreversible electroporation. J Urol

180(6):2668–2674.

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organisms. I. Killing of bacteria and yeast. Biochim Biophys Acta

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Stopper H, Zimmermann U, Wecker E. 1985. High yields of DNA-transfer

into mouse L-cells by electropermeabilization. Z Naturforsch

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XXXQ12 F. Fernand, L. Rubinsky, A. Golberg*,B. Rubinsky. . . . . . . . . . . . xx–xx

Variable Electric Fields for HighThroughput Electroporation ProtocolDesign in Curvilinear Coordinates

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