Phenomenological Theory of Low-Voltage Electroporation. Electric Field Calculations Istva ´ n P. Suga ´ r,* ,† James Lindesay, ‡ and Robert E. Schmukler § Departments of Biomathematical Sciences and Physiology/Biophysics, Mount Sinai School of Medicine, New York, New York 10029, Computational Physics Laboratory, Howard UniVersity, Washington, DC 20059, Stanford Linear Accelerator Center, Stanford UniVersity, Stanford, California 94309, Pore 2 Bioengineering, 19212 Orbit DriVe, Gaithersburg, Maryland 20879, and Drexel UniVersity, Philadelphia, PennsylVania 19104 ReceiVed: October 31, 2002; In Final Form: February 6, 2003 In common electroporators, cells can be transfected with foreign genes by applying a 150-700 V pulse on the cell suspension. Because of Joule heating, the cell survival rate is 10-20% in these elecroporators. In a recently developed electroporator, termed the low-voltage electroporator (LVEP), cells are partially embedded in the pores of a micropore filter. In LVEP, cells can be transfected by applying 25 V or less under normal physiological conditions at room temperature. The large increase in current density in the filter pores, produced by the reduction of current shunt pathways around each embedded cell, amplifies 1000-fold the local electric field across the filter and results in a high-enough transmembrane voltage for cell electroporation. The Joule heat generated in the filter pore is quickly dissipated toward the bulk solution on each side of the filter, and thus cell survival in the low-voltage electroporator is very high, about 98%, while the transfection efficiency for embedded cells is above 90%. In this paper, the phenomenological theory of LVEP is developed. The transmembrane voltage is calculated along the membrane of the cell for three different cell geometries. The cell is either fully, partially, or not embedded in the filter pore. By means of the calculated transmembrane voltage, the distribution of electropores along the cell membrane is estimated. In agreement with the experimental results, cells partially embedded in the filter pore can be electroporated by as low as 1.8-3.5 V of applied voltage. In the case of 25 V applied voltage, 90% of the cell surface can be electroporated if the cell penetrates further than half of the length of the filter pore. 1. Introduction Biological membranes are known to become transiently more permeable by the action of short electric field pulses 1-4 when the threshold value of the transmembrane voltage, about 0.5-1 V, is exceeded. (The transmembrane voltage is defined by the potential difference between the inner and outer surfaces of the cell membrane.) This phenomenon is called electroporation or electropermeabilization, and it can be used to transfect cells with foreign genes. 5 Electroporation of biological cells is commonly carried out in a cell suspension using a parallel plate capacitor chamber. 6 The field between the plates is essentially homoge- neous because the cell density is low. The voltage required for electroporation varies from 150 to 700 V across a 0.2 cm gap of physiologic solution (∼0.15 M NaCl). The applied voltage depends on factors such as the spacing between the capacitor plates, the cell type, and solution temperature. The field strengths needed for suspension electroporation normally vary between 750 and 2000 V/cm. The resulting current produced by these fields in the low-resistivity physiologic solution is in the range of 25-100 A. Substantial Joule heating, electrode products, and solution electrolysis are byproducts produced by these fields in cell suspension, 7 and thus the cell survival rate is low. For COS-7 cells, the survival rate in suspension experiments varies from 10% (ref 8) to 20% (ref 9). These survival rates are in agreement with the rates quoted by commercial companies for their systems (personal communications with BTX Corp., Life Technologies, Inc., and Savant/E-C Apparatus, Inc.) Recently, an alternative to cell suspension electroporation (SEP), the method of low-voltage electroporation (LVEP), was introduced. 10-16 A schematic of the low-voltage electroporator (LVEP) is shown in Figure 1. 17 The vertical chamber consists of two mirror-image halves. The inside diameter of the cylindrical chamber is 1 cm, and cylindrical porous carbon electrodes enclose the upper and lower ends of the chamber. The carbon electrodes apply the input signal and are separated by 2 cm. This produces a cylindrical measurement volume with dimension of 1 cm in diameter and 2 cm in length. A polycarbonate Nuclepore filter (its plane aligned perpendicular to the symmetry axis of the chamber) is sealed into the center of the chamber, and the cells are then embedded in the filter pores (see enlargement in Figure 1) by using a hydrostatic pressure of 25-30 mmHg. In LVEP, as low as 2-25 V of applied voltage is sufficient to induce electroporation because 40% of the applied voltage drops in the 13 μm long micropores of the filter. 17 The average field across the entire chamber for 10 V input is less than 5 V/cm, while the average field across the filter with cells is about 3000 V/cm. Thus, the field in a LVEP is highly inhomogeneous, amplified about 1000 times in conjuntion with the increase in current density through the filter pores. However, the current produced in this system is only 25-50 mA. The bulk temperature increase caused by a 90 ms pulse of 10 V is less than 0.003 °C, and the local Joule heating generated in the filter pore is dissipated in less than 0.3 ms (ref 16). Because of the negligibly small Joule heating, the cell survival rate is about 98% (refs 12 and 16). The development of the phenomenological theory of SEP started 30 years ago. The transmembrane voltage around a † Mount Sinai School of Medicine. ‡ Howard University and Stanford University. § Pore 2 Bioengineering and Drexel University. 3862 J. Phys. Chem. B 2003, 107, 3862-3870 10.1021/jp022343k CCC: $25.00 © 2003 American Chemical Society Published on Web 03/26/2003