A biophysical phenomenon due to electromagnetic fields

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1 Radio Science, Volume 30, Number 1, Pages , January-February 1995 Electroporation in cells and tissues: A biophysical phenomenon due to electromagnetic fields James C. Weaver Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology Cambridge Abstract. The effect of "strong" electromagnetic fields on cells and tissue can be dramatic but not necessarily harmful. The essentially universal biophysical phenomenon of "electroporation" occurs if an applied field causes the cell transmembrane voltage to reach about V in a time of microseconds to milliseconds. Ordinarily the cell membrane is a formidable barrier to the transport of ions and charged molecules. However, electroporation results in a large increase in transmembrane conductance, which is believed to be caused by ion transport through temporary membrane openings ("pores"). This high-conductance state limits the transmembrane voltage and thereby protects the membrane. A large increase in molecular transport generally occurs for the same conditions and allows polar molecules to be introduced into cells. Similar enhanced molecular transport can be caused in living tissues. Not only cell membranes, but also cell layers or even the stratum corneum of human skin can be temporarily altered by the electrical creation of aqueous pathways. The mechanism of electroporation is partially understood, in that the electrical and mechanical behavior of artificial planar bilayer membranes can be described quantitatively by a theoretical model based on transient aqueous pores. More complex behavior in cell membranes may be due to both the complicated shapes of cell membranes and the additional participation of metastable pores and interactions with cell structures. In the case of tissues the situation is even more complex and has only recently begun to be studied but has the prospect of providing a new approach to transporting polar molecules across tissue barriers. 1. Introduction Electropotation is believed to be the rapid creation of aqueous pathways through lipid-containing barriers in cells and tissue. The driving force is the physical interaction of electric fields with two deformable materials with different dielectric con- stants, K: (1) lipids, with K 2-3 and (2) aqueous electrolytes, with K e = = Kw, where e denotes electrolyte and w water. Most investigations to date have involved cell and artificial planar bilayer membranes, but recently, exploration of tissue electroporation has begun. Individual lipidcontaining bilayer membranes have a thickness of h 3 to 7 x 10-9 m. As illustrated in Figure 1, this thin, low dielectric constant region presents a large barrier (of the order of 100 kt) to the transport of even univalent ions (z = 1; q = e = 1.6 x C). Copyfight 1995 by the American Geophysical Union. Paper number 94RS /95/94RS This fundamental barrier function to molecular transport is important to defining the intracellular region of a cell. The ability to use a physical stimulus (a "strong" electric field pulse) to compromise this barrier is of considerable significance, as it may allow "drug delivery" into otherwise inaccessible compartments within biological systems. Although this is not yet a large subfield of investigation, there have already been many studies of the effects associated with electroporation [Neumann et al., 1989; Tsong, 1991; Chang et al., 1992; Weaver, 1993; Orlowski and Mir, 1993; Blank, 1993]. Cell manipulation in vitro based on DNA introduction is presently the most common use. However, electroporation of cells in vitro can also be used for (1) introduction of enzymes, antibodies, and other biochemical reagents for intracellular assays, (2) selective biochemical loading of one size cell in the presence of many smaller cells, (3) introduction of virus and other particles, (4) insertion of membrane macromolecules into the cell membrane, and (5) cell killing under nontoxic con- 205

2 206 WEAVER: ELECTROPORATION IN CELLS AND TISSUES = Ansoft Calculations o = Parsegian's Calculations ,o,,,,o Displacement nm Figure 1. Numerical calculation of the Born energy barrier for transport of a charged sphere across a membrane (thickness d = 7 nm. The numerical solution was obtained by using commercially available software (Ansoft, Inc., Pittsburgh, Penn.) to solve Poisson's equation for a continuum model consisting of a circular patch of low dielectric constant material (K m --- 2) immersed in water (K w = 80). The ion was represented by a charged sphere of radius r s = 0.2 nm and positioned at a number of different displacements on the axis of rotation of the disc. No pore was present. The electric field and the corresponding electrostatic energy were computed for each case to obtain the values plotted here as a solid line (Ansoft calculations). The three values denoted by o (Parsegian's calculations) are from his paper [Parsegian, 1969], with the largest lying just under the Ansoft peak. As suggested by the simple estimate of equation (2), the barrier is large, viz., AW 2.8 x J 65 kt. As is well appreciated, this effectively rules out significant spontaneous ion transport. The appearance of aqueous pathways ("pores," Figure 2) provides a large reduction in this barrier (Weaver [1994], reprinted with permission). ditions. While less emphasized to date, tissue electroporation has begun to be investigated, as there are potentially significant applications, which include (1) enhanced cancer tumor chemotherapy, (2) transdermal drug delivery, (3) noninvasive sampling for biochemical measurement, and (4) localized in situ gene therapy. Conditions and Consequences of Reversible Electrical Breakdown According to present understanding, electroporation universally occurs in all cell and artificial planar bilayer membranes. Generally, short pulses (microsecond to millisecond) are used, with electroporation occurring when the transmembrane voltage, U(t), reaches about V. This is well above the normal "resting potential" ( 0.1 V) developed by living cells. For isolated cells the electric field pulse amplitude (this refers to the value in the extracellu- lar aqueous medium, not air) is V/m. Such field pulses lead to a high conductance state, which has been termed "reversible electrical breakdown" (REB), even though no true breakdown occurs. The maximum energy available to a monovalent ion or molecule for U 1 V is only about 1 ev, which is too small to ionize most molecules, and therefore cannot lead to conventional avalanche breakdown [Lillie, 1958]. REB involves a rapid membrane discharge, in which the large U(t) returns to low values a few microseconds after the pulse ends. However, complete membrane recovery can be orders of magnitude slower, i.e., seconds to minutes. Most signifi-

3 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 207 (A) (B) (C) (D) (E) (F) Figure 2. Drawings of hypothetical structures for transient and metastable membrane conformations which are believed relevant to electroporation. (a) free volume fluctuation; (b) aqueous protrusion or "dimple"; (c) hydrophobic pore; (d) hydrophilic pores, which are usually regarded as the "primary pores" through which ion and molecules pass; (e) composite pore with one or more proteins at the pore's inner edge; (f) composite pore with "foot-in-the-door" charged macromolecule inserted into a hydrophilic pore. The transient aqueous pore model assumes that transitions from a -- b -- c or d occur with increasing frequency as U is increased. Type e may form by entry of a tethered macromolecule while the transmembrane voltage is significantly elevated, and then persist after U has decayed to a small value through pore conduction. It is emphasized that these hypothetical structures have not been directly observed and that support for them derives from interpretation of a variety of experiments involving electrical, optical, mechanical, and molecular transport behavior. (From "Electroporation: A general phenomenon for manipulating cells and tissue," by J. C. Weaver, Journal of Cellular Biochemistry. Copyright 1993 by Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc. Reprinted with permission.) cantly, pulse conditions associated with REB appear to be the same as those associated with a tremendous increase in molecular transport into cells. Early studies using such pulses found both irreversible [Sale and Hamilton, 1967] and reversible [Neumann and Rosenheck, 1972] effects in cells, with some giving evidence for involvement of some type of pore [Kinosita and Tsong, 1977]. Additional investigations used artificial planar bilayer membranes to show that irreversible effects generally occurred in these simpler systems [Abidor et al., 1979; Chernomordik et al., 1983, 1987; Chernomordik and Chizmadzhev, 1989]. However, some types of planar membranes (e.g., oxidized cholesterol and membranes stabilized by uranyl ions) exhibited both irreversible and reversible effects [Benz et al., 1979; Abidor et al., 1982]. Membrane Structural Changes Are Responsible for Electroporation The present view is that electroporation is a rapid process of structural rearrangement within the membrane (Figure 2), such that aqueous perforations appear [Abidor et al., 1979]. For example, optical measurements support the idea that some type of rapid membrane structural rearrangement occurs, coincident with membrane conductance changes, which is consistent with pore formation [Neumann et al., 1992]. This is consistent with theoretical models based on physical interactions, in which an increased transmembrane voltage favors entry of water (large dielectric constant) into the membrane (low dielectric constant) [Abidor et al., 1979; Weaver and Mintzer, 1981; Sugar, 1981]. From a purely physical perspective, membrane

4 208 WEAVER: ELECTROPORATION IN CELLS AND TISSUES conformational changes are general and can be expected as U is increased due to the combination of deterministic electrostatic interactions and sto- chastic thermal fluctuations [Weaver, 1992]. Nontransport Consequences of E!ectroporation Two other electroporation-related phenomena have been discovered that extend beyond the scope of transport of ions and molecules across the membrane. The first is electrofusion, in which the membranes and contents of cells are merged [Sowers, 1989]. Electrofusion generally occurs for electric field pulsing conditions close to those that cause REB, but in which the cells are physically contacted before or after the pulsing. The second is electroinsertion [Mouneimne et al., 1989; Zeira et al., 1991], in which proteins that have the necessary characteristics to reside stably in a membrane (e.g., suitable regions of hydrophobicity and regions of charge) can be inserted into the membrane by electric field pulses similar to those that cause REB. Thus the occurrence of pores caused by electric field pulses has several types of consequences that have been observed experimentally. With this in mind the term "electroporation" is used to denote the hypothesis that aqueous pathways ("pores") are created by an elevated transmembrane voltage. Common to all of these terms is the idea that the natural barrier function of a membrane is over- come, so that ions and water-soluble molecules can readily cross the membrane. Although the microscopic mechanism by which molecular transport occurs is not yet established, there has been significant progress in understanding electrical behavior (voltage, conductance, and capacitance of the membrane) and mechanical behavior (recovery or rapture of planar membranes) and some progress in understanding molecular transport (numbers of molecules that cross the membrane). However, there has been relatively little progress in understanding membrane recovery (restoration of the barrier as time progresses) and ultimate cell fate (survival or death). 2. E!ectroporation Mechanism The appearance of pores is believed to involve the stochastic creation of microscopic pores, with contributions from both "kt energy" (stochastic, associated with fundamental thermal fluctuations) and electrical energy (deterministic, associated with the elevated transmembrane voltage) [Abidor et al., 1979; Weaver and Mintzer, 1981; Sugar, 1981]. These "primary" pores are thought to be transient (Figure 2). As pores are created and then expand, they are believed to have fluctuating sizes. Thus a range of pore sizes (a "pore population") is expected [Barnett and Weaver, 1991; Weaver and Barnett, 1992]. Cell membranes are more complex than artificial planar bilayer membranes, so that interactions of transient aqueous pores with other molecules (e.g., protruding cytoplasmic macromolecules) and cellular structures (e.g., the cytoskeleton) are also possible and may lead to metastable pores which persist long after the membrane discharges (within microseconds of a pulse). Primary and Secondary Pores Transient aqueous pores appearing within the phospholipid portion of the cell membrane are believed to be the "primary pores," i.e., those that govern the membrane's electrical behavior and molecular transport. These are thought to be "hydrophilic pores" [Abidor et al., 1979], with a minimum radius of about 1 nm [Barnett and Weaver, 1991]. As noted above, because of their stochastic origin, a distribution of sizes up to several times this is expected. These primary pores are not likely to be imaged by any known form of microscopy because of their small size, fluctuating and transient nature, and the lack of a suitable contrast mechanism (the membrane is a thin fluid layer of low z material which is bathed by aqueous saline). Our understanding of primary pores is therefore expected to be inferred from their ionic and molecular transport properties [Weaver, 1994]. Attempts to use electron microscopy have been reported. The striking, very large pores observed in erythrocyte membranes are now believed to be secondary pores, perhaps caused by enlarging primary pores by pressuredriven flow [Chang, 1992], since they are much too large and appear long after membranes are known to discharge because of REB. Thus our present view of cell membrane electroporation is that a large but transient population of primary hydrophilic pores is created, and this population dominates the electrical behavior of the membrane. In addition, however, secondary pores are likely to be created from some of the primary pores, either by "trapping" of large primary pores through interaction of cellular structures or molecules or by other driving forces, such as osmotically

5 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 209 generated flows. At the present time the primary pore population can be understood in terms of physical models, but there is relatively little quantitative understanding of secondary pores. Pore Formation Membranes are microscopic systems and therefore experience significant fluctuations [Lipowsky, 1991]. In the case of a phospholipid bilayer, those with most relevance to electropotation are the membrane conformational fluctuations that involve entry of water and water-soluble molecules into the membrane. According to the transient aqueous pore hypothesis, the energy needed to form an aqueous pore is (e - e ) U2 f r E(r, U) = 2st 7r - srfr 2 - h 2 a 2r dr J rmin where is a function of the pore size and internal conductivity [P tu henko nd Ch&m d h½, 1982; Barnett and Weaver, 1991], F is the surface energy density of the membrane-water interface, and 7 is the pore edge energy. The stochastic entry of, and departure from, water into a pore governs pore evolution [Powell and Weaver, 1986; Toner and Cravalho, 1990]. This in turn ensures that a distribution of pore sizes will be present. Indeed, use of a transient aqueous pore theory that can quantitatively explain much of the electrical behavior for short pulses fundamentally and explicitly involves a heterogeneous pore population. As illustrated in Figure 2, several types of pores have been suggested. Hydrophobic pores are assumed to form first, with transitions to hydrophilic pores (the "primary pores") at larger r because the energy cost to make the pore circumference ("edge energy") is much larger than that for hydrophilic pores. This is easy to understand qualitatively: the interfacial energy for the hydrocarbon chains and water is much larger than that for the head groups and water. The hydrophilic pores are believed to be metastable over short time scales. Composite pores involving membrane proteins may also be possible and may have smaller effective values of "edge energy" and longer metastable lifetimes. Entry of transported or of cell-attached intracellular molecules into a pore may prevent pores from shrinking, due to electrostatic repulsion, also leading to longlifetime pores. Finally, secondary very large pores (1) may evolve from the primary transient aqueous pores because of pressure-driven flows. Vesicles and cells are separated from the external medium by a closed membrane, so that interfacial polarization plays an important role by causing large changes in the transmembrane voltage, A U(t), by external electric field changes, AE(t). The case of an isolated spherical membrane with constant membrane conductivity (i.e., no pores present) is well known to have AU described by AU(t) = 1.5E(t)Rcell cos 0 (2) Here, Rc½ u is the cell's radius, 0 is the angle between the applied electric field, E(t), and the site on the cell membrane at which U is measured. Generalizations of this equation to nonspherical shapes also predict a significant dependence on cell size. Thus unlike the exposure of cells and tissue to chemicals (usually involving only chemical concentration magnitudes and exposure times, but seldom concentration gradients), exposure to electric fields fundamentally involves the vectorial nature of the field (magnitude and direction). This leads to many more possible "exposure" conditions at the individual cell level for the same externally applied electric field [Weaver and Astumian, 1992]. Equation (2) is valid only for small electric fields, viz., those that result in negligible electroporation, because the appearance of conducting pores causes a significant change in the membrane conductivity, and this occurs preferentially at the "poles" of the cell, i.e., the regions for which cos 0 -- ñ 1. Equation (2) also provides an amplification, in the sense that a change in the external electric field, c, results in a much larger change, z m, in the transmembrane electric field. Here,/ E m = A U/h, where h is the thickness of the membrane. Because of the Rcell dependence, large cells generally require smaller electric field pulses than small cells. Isolated mammalian cells with Rcell 10 tam experience electropotation onset for short field pulses of magnitude E 105 V/m. Smaller microorganisms, e.g., bacteria, require a much larger AE to achieve the same AU. Usually, the electric field exposure is brief: short pulses of about 1 /as to long pulses of about 1 ms are common. The degree of electropotation at lower fields and longer times has received much less attention.

6 210 WEAVER: ELECTROPORATION IN CELLS AND TISSUES Nonthermal, Mild Nature of Electroporation demonstrate that conditions causing significant molecular transport do not necessarily result in dam- The basis of electroporation is believed to be an age. electrostatically driven structural rearrangement of the membrane, not heating. Pore formation begins Membrane Damage Due to Electroporation to occur extremely rapidly (estimated to be of the Electric field pulses that are too large or long are found to cause planar membrane destruction and order of 10-8 s or less), before any significant temperature rise occurs. Essentially all of the heating takes place in the extracellular medium, for which the rate of temperature rise is dt/dt are associated with cell killing. In the case of artificial planar bilayer membranes, early nonpore theories [Crowley, 1973] explained neither the crit- ree2/cepw. Typical electric field pulses are in the ical transmembrane voltage nor the stochastic narange V m - and for physiological media ture of rupture in planar membranes. In contrast, a the electrical conductivity is r e 1.4 S m - Ce is stochastic model based on transient aqueous pores the electrolyte specific heat, and p is the mass was successful [Abidor et al., 1979; Weaver and density of water. As a result, dt/dt øC Mintzer, 1981; Sugar, 1981]. As shown in Figure 3, s - but because of the short exposure time the the theoretical estimate of the free energy change temperature rise often is only about IøC per pulse. associated with pore formation (the"pore energy," Electropotation has also been demonstrated in spe- AE(r, U)) is a function of both pore size and cial, low-conductivity media for which the extracel- transmembrane voltage. Significantly, the transient lular heating is significantly smaller, but this may aqueous pore models correctly predict the magnialso change the chemical stress of cells as mole- tude and stochastic nature of planar bilayer memcules from the external medium enter the cell brane rupture. According to the transient aqueous through pores. pore models, for planar membranes, escape of one The term "mild" refers to the notion that even or more large "critical" pores over the pore energy complex, denaturable biological macromolecules barrier, AEma x (Figure 3), is believed to account for should not be altered by the electric field pulses the prompt destruction of such membranes. used to cause electropotation. For typical electro- Cell membranes are topologically different and porating pulses, U(t) reaches values about 5-10 compositionally much more complex than artificial times larger than the normal physiologic value (U planar bilayer membranes. Both features appear to 0.1 V) generated by active ion pumps in the mem- be relevanto cell membrane damage by electropobrane. However, the resulting change A U ration. First, consider the possibility of rupture. It V has an associated energy that is too small to has been hypothesized that a portion of the memdisrupt most molecules. Further, inside a pore the brane, e.g., a region bounded by cytoskeletal elelocal electric field is reduced because of the "focus- ments, can behave like a small planar membrane ing fields" (spreading resistance fields) near the and can therefore exhibit prompt rupture. Second, entrances to a pore. These local fields accelerate a it appears unlikely that a closed membrane, such as charged molecule to only a fraction of the energy a vesicle or cell, can completely rupture, because needed to chemically alter most molecules. At the there is no boundary at which membrane phospholarger electric fields sometimes used to electropo- lipids can accumulate upon expansion of a large rate small microorganisms there is evidence that pore. For this reason the pore energy curve of macromolecules (DNA) in solution can be directly Figure 3 is believed appropriate only for a planar altered, but this does not occur for the smaller membrane. If so, there is no such boundary, and for electric field pulses used with the larger eukaryotes this reason no opportunity for the membrane to [Sabelnikov and Cymbalyuk, 1990]. vanish by evolving a large pore which then expands Finally, some biological systems experiencing to that boundary. Instead, larger pores are favored electropotation have clearly experienced negligible for larger transmembrane voltages, but as the memdamage. For example, both electroinsertion of pro- brane discharges through the pores during REB, a teins into red blood cell membranes [Mouneimne et vesicular membrane returns to its initial state [Sugal., 1989] and electroporative loading of platelets ar and Neumann, 1984]. An inability to promptly [Hughes and Crawford, 1989] showed circulating rupture via critical pores should be general for survival times close to controls. Such experiments closed membranes. Neither vesicular membranes

7 WEAVER: ELECTROPORATION IN CELLS AND TISSUES f'''' I'''' I'''' I'''' I' ''' J'''' I'''' I''' 't oo o -too to Radius (nm) Figure 3. Computed plot of the hydrophilic pore formation energy, AE(r, U), versus pore radius, r, for a planar membrane. In order to make the comparison to the average thermal fluctuation energy easier, the pore energy, AE, which is a function of both pore radius, r, and transmembrane voltage, U, is expressed as a ratio to kt, the mean thermal energy. Such "primary pores" (Figure lb) are believed to occur in the bilayer membrane portion of cell membranes. For a planar membrane, pores that expand to radii larger than the barrier peak location (a critical radius, rc) can expand to the boundary of the supporting structure for the membrane (the aperture in a planar membrane experiment; possibly a cytoskeletal element in a cell). This is rupture. Vesicles and cell membranes without a pore/cell structure interaction are not expected to rupture [Sugar and Neumann, 1984]. Instead, cell lysis for large pulses probably involves a secondary response due to chemical imbalances associated with the presence of many pores. (From "Electroporation: A general phenomenon for manipulating cells and tissue," by J. C. Weaver, Journal of Cellular Biochemistry. Copyright 1993 by Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc. Reprinted with permission.) nor cell membranes that are "flee-standing" should exhibit rupture. If, however, the more complex cell membrane has bounded portions that behave like small planar membranes, then these membrane regions may undergo rupture. Moreover, cell membranes may support a variety of long-lifetime metastable pores (e.g., Figure 2), which provide pathways for small ions and molecules that persist long after U(t) has decayed to a small value. Then even very small voltages (<1 mv) may transport significant numbers of charged molecules [Weaver and Barnett, 1992]. Electrical Behavior Most cell electroporation, and some electroporation of artificial planar bilayer membranes, involves short pulses (microseconds to milliseconds). Onset of electroporation-related phenomena then generally occurs when U reaches about V. The scientific literature suggests that this is essentially universal. This means that the onset of electroporation is mainly a physical phenomenon and that membranes of somewhat different composition have these differences overwhelmed by only slight changes in U(t).

8 212 WEAVER: ELECTROPORATION IN CELLS AND TISSUES In the case of artificial planar bilayer membranes, experiments show that the electrical and mechanical behavior involves mechanical destruction (rupture) for moderate values of U (e.g., mv). Strikingly, however, by using short pulses, much larger U can be achieved for some types of membranes, and rupture is then avoided. Instead the membrane achieves a high conductance state and rapidly discharges via REB [Benz et al., 1979; Benz and Zimmermann, 1980a, b]. Longer pulses have also been used in experimental systems that provide "voltage clamp" capability [Sukharev et al., 1983; Glaser et al., 1988]. A short description of electrical behavior is worthwhile, mainly because electroporation is caused by electrical stimuli but also because the extent and progression of electroporation can be followed by electrical measurements. A "signature" of electroporation is the tremendous increase in electrical conduction which can be measured, and which is believed due to ionic conduction through transient aqueous pores. The behavior of the transmembrane voltage, U(t), during membrane charging, and the subsequent appearance and evolution of a pore population, is intimately connected with the number and size of the pores. The success of a transient aqueous pore model in providing a quantitative description of U(t) under these conditions provides confidence that electroporation is a valid concept. Consider a planar membrane experiment that uses a short pulse ("charge injection" conditions) [Benz et al., 1979; Barnett and Weaver, 1991]. As the pulse size is increased, very small pulses simply charge the membrane, which behaves as an ordinary capacitor in series with a fixed resistance, such that the charging time constant is of the order of 1 /as. Somewhat larger pulses bring U to several hundred millivolts, but then the membrane stochastically ruptures. Still larger pulses lead to a larger membrane conductance, G(t), and increasingly faster decay of U(t). This is the origin of reversible behavior. The membrane discharges before a single large pore can evolve, which would then lead to rupture. In theoretical models this is found to accompany the nonlinear appearance of pores of many sizes. The membrane conductance is predicted to become progressively larger for larger pulses, resulting in faster and faster discharge times. This phenomenon is reversible electrical breakdown (REB), which occurs when U(t) reaches about volume [Neumann et al., 1989; Tsong, 1991; Chang et al., 1992; Weaver, 1993]. On the basis of experimental evidence [Benz et al., 1979] and theoretical models [Freeman et al., 1994], less than about 0.1% of the membrane area becomes aqueous during REB. Absence of a Threshold Transmembrane Voltage for Electroporation Onset The onset of detectable electroporation-related phenomena has two basic features: (1) for a given pulse duration the onset occurs at about the same voltage for many types of membranes, and (2) there is no fixed threshold, but instead onset is determined by the history of the transmembrane voltage. First, consistent with the idea that electroporation is a physical process, the onset stage of electroporation is believed to depend mainly on a physical interaction of the transmembrane voltage with the phospholipid regions of the cell membrane. If so, the chemical composition of phospholipids should be relatively unimportant, as differences in chemical composition of the membrane should be overwhelmed by slightly different transmembrane voltages. Thus the literature shows that for single short pulses (microseconds to milliseconds), electroporation onset generally occurs for many types of membranes if the transmembrane voltage reaches about V. Unlike artificial planar bilayer membranes, for which moderate but long-lasting "pulses" cause rupture, the consequences of long-lasting relatively small magnitude pulses for cells and tissues has not been emphasized. Second, the onset of electroporation is consistent with the idea that both time and an elevated trans- membrane voltage are needed for a pore population to evolve sufficiently that the high conductance needed for REB is achieved. Early experiments showed that the transmembrane voltage at which REB occurs in artificial planar bilayer membranes depends on the length of a single rectangular pulse [Benz et al., 1979]. For example, as the duration of a rectangular pulse was increased, the value of U for the onset of REB decreased from about U 1.2 V for a 10-8-s pulse down to about U 0.45 V for a 10-5-s pulse (oxidized cholesterol, 25øC) [Benz and Zimmermann, 1980a]. This behavior is consistent with a transient aqueous pore theory [Powell et al., 1986]. Similarly, experiments with algal cells (Halicystis parvula) revealed that REB onset dropped from U 1.8 V at 5 x 10-6 s to U 0.5

9 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 213 V at 10-4 s [Zimmermann et al., 1981]. Similar behavior has been described by others [Chernomordik, 1992]. With this in mind, the recent claim [Teissie and Rols, 1993] that electroporation onset occurs at A U 0.2 V, independent of pulse duration, is difficult to understand. Most of the experi- mental and theoretical evidence explicitly supports the view that there is no threshold transmembrane voltage and that instead the onset depends on the history of the elevated transmembrane voltage. Molecular Transport The dramatic electrical and mechanical behavior may be of interest to physical scientists, but the real significance of electroporation for biology and medicine lies in its ability to transport polar molecules across cell membrane and tissue barriers. The sci- entific literature shows that for the same conditions that cause REB there is a tremendous increase in molecular transport across cell membranes. Somewhat surprisingly, however, only a few studies have made quantitative determinations of molecular uptake or release [Mir et al., 1988; Chakrabarti et al., 1989; Lambert et al., 1990], especially in terms of the "number of molecules per cell" [Bartoletti et al., 1989; Prausnitz, 1993a; E. A. Gift and J. C. Weaver, Observation of extremely heterogeneous electroporative uptake which changes with electric field pulse amplitude in $accharomyces cerevisiae, submitted to Biochimica et Biophysica Acta, 1994, hereinafter referred to as Gift and Weaver, submitted manuscript, 1994]. Introduction of DNA into cells has dominated electroporation applications. In this general application, DNA is added to a preparation that consists of a large number (e.g., ) of cells. The cell population is electrically pulsed, and a small subpopulation of cells is obtained that has successfully (1) taken up at least one molecule of DNA, (2) incorporated the DNA so that it is functional, and (3) survived. The latter is usually related to the introduced DNA, in that a gene for antibiotic resistance is included, so that a "selective medium" containing that antibiotic can be used, with the powerful result that only cells that have the antibiotic resistance gene can survive and grow. Even if only a few cells are obtained, the protocol is often an overall success, because these cells can be "amplified" almost arbitrarily by growth. For this reason, although relatively simple and powerful, this technique does not require careful attention to the mechanism of electroporation, or the optimal conditions for cell recovery and survival. However, it is now becoming clear that many other applications are possible but that these will require more appreciation of mechanism and of the optimal conditions for molecular uptake and cell survival. It is likely that almost any type of molecule can be introduced into cells by electroporation. Large numbers of smaller molecules can also be intro- duced into cells, and this suggests widespread potential applications (Table 2), even though the detailed molecular transport mechanism is not fully understood. At the microscopic level, candidate transport mechanisms include electrical drift (electrophoresis), electroosmosis (electrically driven flow), diffusion, and endocytosis. The first three mechanisms can clearly lead to increased molecular transport for water-soluble molecules if pores are involved, but it is not clear whether endocytosis is a primary field-stimulated membrane process or a secondary cell-stimulated process that occurs for chemically unbalanced cells following electroporation. In order to better understand the basic nature of electroporation, and also for many applications, it will be important to know the order of magnitude of molecular transport. The molecular size, shape, and charge can all be expected to be of interest, as direct interaction of molecules with pores may involve all three of these properties. Simple exclusion by geometric size ("sieving") is the simplest hypothesis that can be considered, but distortions of the pore by a nearby or entering molecule may also occur. Similarly, the shape of a molecule, particularly if a molecule is long, should be impor-' tant (e.g., Figure 2f). Electrostatic exclusion because of a Born energy repulsion associated with the lower dielectric constant of the membrane inte- rior regions, and interaction with charged head groups within hydrophilic pores and any composite pores, can also be significant. The evidence to date suggests that electrical drift is the dominant molecular transport mechanism [Klenchin et al., 1991; Sukharev et al., 1992; Weaver and Barnett, 1992; Wang et al., 1993; Prausnitz et al., 1993a]. If so, the very molecules that are ordinarily excluded because of the Born energy barrier of the membrane (Figure 1) are most effectively transported. The reason that electrical drift can be very effective is that not only does the applied electric field, AE, favor the creation and

10 214 WEAVER: ELECTROPORATION IN CELLS AND TISSUES Table 1. Sources of Heterogeneous Electroporation Within Cell Populations Source Cell size Cell shape Cell orientation Field nonuniformity Cell-cell separation Tissue heterogeneity Membrane composition Pore statistical behavior Significance Generalization of equation (2) Generalization of equation (2) Generalization of equation (2) Electric field varies within chamber Perturbation of local field by nearby cells Perturbation of local field by tissue Composition variation within cell population* Electroporation is fundamentally stochastic (kt fluctuations) From Weaver and Barnett [1992]. *The observed universality of electroporation onset at about U I V argues against significant membrane composition effects, but minor contributions to heterogeneity may be due to membrane properties. Much greater variation is expected after the pulse, i.e., during the membrane recovery phase, when transmembrane voltage effects are greatly reduced. evolution of a pore population, but the current flowing through the pores also provides a direct transporting force. Moreover, the local electric field near the pore entrances is nonuniform and should focus electrophoretic transport into the pores. A better understanding of electroporative molecular transport is clearly important. The notion that one can access the cell interior by introducing (or removing) molecules that are normally retained by the membrane is general and powerful. Tissue E!ectroporation The great majority of the investigation and use of electroporation has been concerned with isolated cells in vitro. In comparison, the extension of electroporation to intact tissues has only recently begun. Although the potential applications of tissue electroporation are large, only a few studies have been reported. Some studies have emphasized immediate electrical measurements [Powell et al., 1989] or combined molecular transport and electrical measurements [Prausnitz et al., 1993b], while others have focused on important but time-delayed biological consequences of molecular transport [Okino and Mohri, 1987; Titornirov et al., 1991;Mir et al., 1991, 1992; Okino et al., 1992; Salford et al., 1993]. The fundamentally compelling attributes of tissue electroporation are that a chemical result is achieved by a readily controlled physical process, that a variety of different chemicals can be used with the same physical process, and that unlike "chemical enhancers" for increased drug delivery, no chemical residue is left behind. The possibility of control is particularly tantalizing, because the ability to assess tissue before and after pulsing by electrical measurements should provide the basis for tailored control of the pulses applied to the tissue. Heterogeneity of E!ectroporation Within a Cell Population It was argued above that the onset of electroporation is essentially universal. However, this does not mean that all of the cells within a population of cells exhibit the same behavior. In fact, there are fundamental reasons for expecting the individual cells within a population to have a distribution of electroporation behavior, mainly because the change in transmembrane voltage due to an external field is expected to be different for different cells (Table 1). Specifically, equation (1) (and its generalizations to nonspherical cells) indicates that vari- ations in cell size, shape, and orientation are important in determining the magnitude of the transmembrane voltage change, A U(t), at different sites on a cell membrane. Cell populations are also well known to exhibit cell-to-cell variations in composition and function ("biological variability"), which may be very important for postpulse phenomena, e.g., membrane recovery. It is therefore not surprising that electroporative phenomena (e.g., molecular uptake and survival) are found to vary for the individual cells within an electrically pulsed population [Weaver et al., 1988; Gift and Weaver, submitted manuscript, 1994]. Rare E!ectroporation Due to Low-Level, Multiple Pulses Almost all studies of cell and tissue electroporation have focused on the use of single, large electric field pulses. However, a few isolated cell electroporative uptake studies [Hashirnoto et al., 1985; Ueda et al., 1991; Stopper et al., 1987; Brown et al., 1992; Prausnitz et al., 1994] and tissue electropora- tion investigations have used multiple pulses [Mir et al., 1991; Prausnitz et al., 1993b]. Similarly, only a few studies have used relatively small electric field strengths in experiments for which uptake was sought [Xie and Tsong, 1990]. Thus multiple-pulse, lower field strength electroporation has been mostly

11 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 215 neglected for applications of electroporation. Moreover, the possibility (hypothesis) that multiple pulses at very low field strengths could cause "rare electroporation", i.e., electroporation of a small subpopulation of cells, has not been emphasized as a candidate for environmental electric and magnetic field effects. This possibility is briefly discussed below, within the context of a general hypothesis involving combined chemical and electric and magnetic field exposures. A General Environmental Hypothesis Involving Both Chemical and Electric and Magnetic Field Exposures A broad-ranging hypothesis for possible biological effects (including human health hazards) considers combined environmental exposures to chemicals and to electric and magnetic fields. Here we briefly consider the more specific subhypothesis that transient magnetic fields cause stimulated uptake of otherwise impermeant molecules. Exposure of humans to toxic chemicals is a well-established environmental hazard and has been the focus of considerable research and regulatory activity. An expanded general hypothesis is that the toxic effects of some environmental chemicals are enhanced because of simultaneous or subsequent exposure to electric and magnetic fields. Although direct field modulation of local chemical reaction rates could be considered, a much larger effect may occur if fields provide access of foreign chemicals to intracellular reaction sites. Environmental electric and magnetic fields have also been the source of persistent interest and considerable controversy, based on the hypothesis that human health hazards may exist. But the possible mechanisms of field interactions with cells and tissue at "weak field" conditions are not well established. Furthermore, most attention has been given to the steady 50- and 60-Hz sinusoidal fields that are associated with power distribution systems [Polk, 1991; Poole and Trichopoulos, 1991; Sagan, 1992; Phillips, 1993; Blank, 1993]. Small Cell Subpopulations With Stimulated Uptake of Foreign Molecules With this in mind, the hypothesis that transient electric and magnetic fields may cause uptake of foreign molecules that are present because of a previous chemical exposure is worth considering. These potentially toxic molecules may not be the usual toxic molecules, since recognized toxic mol- ecules are generally lipophilic and readily permeate cell membranes. The hypothesis is motivated by the following considerations: (1) Alteration of a very small subpopulation of cells, Nmin, can have significant biological consequences. In the extreme case of mutations, alteration of only one cell can be significant. Chemical-induced mutations are well known; in this case the required energy originates from chemical free energy. Thus if a transient magnetic field can cause molecular uptake of an external mutagen, a significant biological effect is achieved, but the energy involved in mutation comes mainly from chemical free energy, not field energy. (2) Recent findings of residential magnetic field transients of many different types, some of which have relatively large magnetic fields (B) and/or time rates of change (db/dt) [Guttman et al., 1994; Thansadote et al., 1993]. Still larger values may occur, but far less often, and could cause uptake even if they are rare. (3) Rare human diseases are considered in epidemiological studies that involve environmental electric and magnetic fields [Sagan, 1992; Phillips, 1993; Blank, 1993]. A requirement that both a prior chemical exposure and a magnetic field exposure occur will decrease the frequency of occurrence of any effects, with only chemically exposed individuals susceptible. (4) Rare but large transients could exceed endogenous fields (fundamental noise plus biologically generated fields) [Weaver, 1992]) within the human body, and thereby overcome a fundamental objection that endogenous fields are usually believed to be much larger than those caused by environmental fields. (5) As suggested below, transient magnetic fields may cause stimulated uptake by cells. Transient magnetic fields can be considered from two viewpoints: (1) interactions with magnetic material, particularly biological magnetite [Kirschvink, 1992], which are direct magnetic field effects, and (2) induction of electric fields, particularly those that result in altered transmembrane voltages, which are electric field effects. In the case of direct magnetic field interactions for very large B, large rotational displacements of magnetite may cause membrane openings due to mechanical perturbation of cell membranes. This would represent an extension of mechanically stimulated uptake [McNeil, 1989; Clarke and McNeil, 1992]. In the case of indirect magnetic field interactions there are two known possibilities for electric field stimulated uptake of impermeant molecules: (1) electroporation

12 216 WEAVER: ELECTROPORATION IN CELLS AND TISSUES and (2) modulation of active cell membrane transport processes. In the first case, infrequent electroporation may occur, given the stochastic nature of pore formation and, more important, the possibility that reduced pore formation energy may occur in association with phospholipid/protein boundaries. In the second case, cells are known to use chemical energy to carry out active transport across cell membranes, which has led to development of theories for electroconformational coupling [Tsong et al., 1989], which is a general process involving membrane enzymes, and results in transmembrane voltage modulation of transport across cell membranes. Very Small Cell Alteration Probabilities and Rates Are Potentially Significant The single-cell alteration probabilities and rates that are consistent with this hypothesis are very small, because alteration of a subpopulation of Nmi n cells can significantly affect a biological system. In principle, even alteration of a single cell (Nmi n = 1) due to entry of foreign molecules could be significant. For a simple estimate the rate of occurrence of cell alteration is written as / a = / t NcellPcell (3) where v a is the rate of altered cells, vt is the rate of transients, here assumed identical, Ncell is the number of cells in the biological system, and Pcell is the probability of alteration of a single cell by a transient. If some minimum number of cells, Nmi n, is altered, then an effect on the entire biological system is presumed to occur. As a first illustration, we estimate the rate of uptake events due to "whole-body" magnetic field transients that causes alteration of the order of 1 million cells (Nmi n 106) per year (exposure time tex p 3 x 107 s) within the human body ( 10 TM cells). In order for this to occur, the necessary product of b, t and Pcell is PtPcell = Nmin 10 6 Ncelltexp (1014)(3 x 107 s) 3 x whole-body transients S -1 (4) Thus the rate of effective transients could be very small and yet significant. As a second illustration we consider the case of a highly localized transient source, such as a "dimer switch," that produces "transients" at the power frequency rate (60 Hz U.S., 50 Hz Europe). Specifically, we assume that a 1-mL tissue volume is exposed, i.e., Ncell 109 cells. We also use the plausible exposure time of the order of 100 s/day, so that the number of "transients" in one year is N t (365)(100 s)(60 transients s - ) = 2 x 106 transients. This means that if again Nmin = 106, a 0.1% subpopulation in this localized volume is altered, and the required probability of cell alteration per transient need be only Nmin Nmin Pcell = = Ncell v t texp Ncell Nt X (5) (109)(2 x 106) In these order-of-magnitude estimates, clearly the parameters vt, Pcell and Nmi n are important. Most of our ignorance is contained in these parameters, particularly Pt and Pcell. Physical monitoring and surveys of field transients should determine the spectrum of environmental transients [Guttman et al., 1993; Thansadote et al., 1993], which here is represented by only a simple mean rate, vt. The parameter Pcell is expected to be much more complex, as it should depend on the transient magnitude and time dependence, the cell type and biological state, and the type and concentration of foreign molecule. Thus extremely small cell participation probabilities or rates are arguably of potential significance. These estimates serve to illustrate the unexplored hypothesis that field stimulated "rare uptake" events might be significant for complex biological systems composed of a large number of cells, e.g., the human body. With this in mind, it is interesting that to date there has been essentially no investigation of electroporation, or other field-stimulated uptake processes, that involve very small subpop- ulations. 3. Postpulse E!ectroporation Effects Membrane Recovery It was argued above that the transmembrane voltage change experienced by the individual members of a cell population should be different because of a distribution of cell sizes, shapes, and orientations (Table 1). The reasoning is that electroporation is believed to be a strong, nonlinear function of

13 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 217 the magnitude and history of U(t). Here we note that the contraction and disappearance of pores can also vary during the recovery phase, after the transmembrane voltage has returned to small values. In this case, however, the biochemical nature of the membrane should be relatively more important. Moreover, the consequence of having many pores may vary from one membrane to another. For artificial planar bilayer membranes some membranes may rupture more readily than others, due to differences in surface and edge energies. For cells, postpulse behavior can vary significantly. For example, some primary pores may expand into very large pores by secondary processes that are particular to the cell type and the experimental conditions. As another example, some experiments show a long-term (seconds to minutes) persistence of molecular transport in a subpopulation of cells within a large population of cells. Although presumably important to the fate of pulsed cells (see below), the postpulse processes that follow decay of U(t) to low levels after REB are not yet well studied. Cell Stress and Death In addition to transport of desired molecules (e.g., DNA added to a cell suspension), an associated cell stress commonly occurs, probably because of chemical influxes and effluxes leading to chemical imbalances, which also contribute to eventual survival or death. If so, the ratio of extracellular to intracellular volume Rvo 1 --= Vextracellular/Vintracellula r should be important. This in turn suggests that in vitro protocols (large ratio) should cause more taxing conditions than tissue electroporation [Weaver, 1994]. For the same electric field pulsing conditions, one cell type may mostly survive while another may be mostly killed. A general trend is found in the use of electroporation to introduce molecules into cells. For a given pulse shape, small-magnitude pulses Table 2. tions cause no effect, but at about 105 V/m (mammalian 4. Summary cells, short pulses) some cells experience molecular uptake. As larger electric fields are used, the percentage of participating cells increases, but the percentage of surviving cells simultaneously decreases. Eventually, for very large fields, essentially no cells survive. Why does this occur? There are at least two hypotheses: (1) a prompt membrane rupture occurs in some portions of the cell membrane, leading to a large hole in the membrane, and Existing and Likely Electroporation Applica- Existing DNA introduction Loading drugs into cells In situ enzymology (load reagents) Insertion of proteins into membranes Tumor tissue drug delivery Localized gene therapy Isolated cell fusion* Likely Low-energy cell killing Loading dyes and tracers into cells Intracellular immunoassays Release of intracellular compounds Transdermal drug delivery Noninvasive tissue sampling Cell/tissue fusion* *The many possible applications of cell fusion by electric fields are worthy of an entirely separate discussion. (2) chemical imbalances occur, due to the influx and efflux through both transient and metastable pores. Although important to almost all applications, a good understanding of cell stress and resultant cell death does not yet exist. Very early studies demonstrated nonthermal killing of microorganisms by electric field pulses which are now associated with electroporation [Sale and Hamilton, 1967]. Much more recently, compelling evidence has been gathered that electroporation plays an important role in cell death and the associated tissue damage of electrocution injury [Lee and Kolodney, 1987] and that membrane recovery can be significantly improved by providing a nonionic surfactant [Lee et al., 1992]. Similarly, it has been suggested that some cells near the stimu- lating electrodes may be killed during defibrillation interventions [Tung, 1992]. Thus although the primary events associated with cell electroporation are mild, the eventual result can be reversible or irreversible, with the latter equivalent to eventual cell death. As wider applications of electroporation are sought, understanding of the postpulse processes will become essential. Electroporation is of compelling interest for two reasons: (1) fundamental aspects of membrane structure and behavior are involved, so that the associated biophysics is of interest as a basic topic, and (2) significant applications in biological research, biotechnology and medicine have been identified (Table 2). Electroporation achieves a chemical and biological result by a physical means, and this means that unlike chemical manipulations

14 218 WEAVER: ELECTROPORATION IN CELLS AND TISSUES of biological systems there is no chemical residue. Further, the fact that electrical phenomena are involved carries the implication that electronic systems can be used to measure tissue impedance before and after pulsing and to control the pulses. Thus in tissue electroporation, rapid electrical measurements allow the occurrence and aftereffects of electroporation to be monitored. In spite of the perceived promise of electroporation there are many aspects of electroporation which are still poorly understood. In this sense, even though the initial studies date back approxi- mately 20 years, investigation of electroporation is still at an early stage. Nevertheless, electroporation is increasingly regarded as compelling, because electrical stimuli can be used to universally alter the natural barrier function of cell membranes and of tissues whose primary barrier is lipid based. For this reason it is expected that the study and application of electroporation will receive increasing attention. Acknowledgments. Stimulating and critical discussions with M. Zahn, J. Zahn, A. Sastra, M. R. Prausnitz, U. Pliquett, J. W. Lin, R. I. Kavet, J. L. Guttman, E. A. Gift, Y. Chizmadzhev, V. G. Bose, S. K. Burns, and R. D. Astumian are gratefully acknowledged. Supported by Army Research Office grant DAAL03-90-G-0218, NIH grant ES06010, and a computer equipment grant from Stadwerke D/Jsseldorf, D/Jsseldorf, Germany. References Abidor, I. G., V. B. Arakelyan, L. V. Chernomordik, Y. A. Chizmadzhev, V. F. Pastushenko, and M. R. Tarasevich, Electric breakdown of bilayer membranes, I, The main experimental facts and their qualitative discussion, Bioelectrochem. Bioenerg., 6, 37-52, Abidor, I. G., L. V. Chernomordik, S. I. Sukharev, and Y. A. Chizmadzhev, The reversible electrical breakdown of bilayer lipid membranes modified by uranyl ions, Bioelectrochem. Bioenerg., 9, , Barnett, A., and J. C. Weaver, Electroporation: A unified, quantitative theory of reversible electrical breakdown and rupture, Bioelectrochem. Bioenerg., 25, , Bartoletti, D.C., G.I. Harrison, and J. C. Weaver, The number of molecules taken up by electroporated cells: Quantitative determination, FEBS Lett., 256, 4-10, Benz, R., and U. Zimmermann, Relaxation studies on cell membranes and lipid bilayers in the high electric field range, Bioelectrochem. Bioenerg., 7, , 1980a. Benz, R., and U. Zimmermann, Pulse-length dependence of the electrical breakdown in lipid bilayer membranes, Biochim. Biophys. Acta, 597, , 1980b. Benz, R., F. Beckers, and U. Zimmermann, Reversible electrical breakdown of lipid bilayer membranes: A charge-pulse relaxation study, J. Membrane Biol., 48, , Blank, M. (Ed.), Electricity and Magnetism in Biology and Medicine, San Francisco Press, San Francisco, Calif., Brown, R. E., D.C. Bartoletti, K. T. Powell, J. G. Bliss, G.I. Harrison, and J. C. Weaver, Multiple-pulse electroporation: Macromolecule uptake by intact, Saccharomyces Cerevisiae Bioelectrochem. Bioenerg., 28, , Chakrabarti, R., D. E. Wyle, and S. M. Schuster, Transfer of monoclonal antibodies into mammalian cells by electroporation, J. Biol. Chem., 264, 15,494-15,500, Chang, D.C., Structure and dynamics of electric fieldinduced membrane pores as revealed by rapid-freezing electron microscopy, in Guide to Electroporation and Electrofusion, edited by D.C. Chang, B. M. Chassy, J. A. Saunders, and A. E. Sowers, pp. 9-27, Academic, San Diego, Calif., Chang, D.C., B. M. Chassy, J. A. Saunders, and A. E. Sowers, Eds., Guide to Electroporation and Electrofusion, Academic, San Diego, Calif., Chernomordik, L. V., Electropores in lipid bilayers and cell membranes, in Guide to Electroporation and Electrofusion, edited by D.C. Chang, B. M. Chassy, J. A. Saunders, and A. E. Sowers, pp , Academic, San Diego, Calif., Chernomordik, L. V., and Y. A. Chizmadzhev, Electrical breakdown of lipid bilayer membranes: Phenomenology and mechanism, in Electroporation and Electrofusion in Cell Biology, edited by E. Neumann, A. E. Sowers, and C. A. Jordan, pp , Plenum, New York, Chernomordik, L. V., S. I. Sukharev, I. G. Abidor, and Y. A. Chizmadzhev, Breakdown of lipid bilayer membranes in an electric field, Biochim. Biophys. Acta, 736, , Chernomordik, L. V., S. I. Sukharev, S. V. Popov, V. F. Pastushenko, A. V. Sokirko, I. G. Abidor, and Y. A. Chizmadzhev, The electrical breakdown of cell and lipid membranes: The similarity of phenomenologies, Biochim. Biophys. Acta, 902, , Clarke, S. F., and P. L. McNeil, Syringe loading intro- duces macromolecules into living mammalian cell cytosol, J. Cell Sci., 102, , Crowley, J. M., Electrical breakdown of bimolecular lipid membranes as an electromechanical instability, Biophys. J., 13, , Freeman, S. A., M. A. Wang, and J. C. Weaver, Theory

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17 WEAVER: ELECTROPORATION IN CELLS AND TISSUES 221 Weaver, J. C., and A. Barnett, Progress towards a theoretical model of electroporation mechanism: Membrane electrical behavior and molecular transport, in Guide to Electroporation and Electrofusion, edited by D.C. Chang, B. M. Chassy, J. A. Saunders, and A. E. Sowers, pp , Academic, San Diego, Calif., Weaver, J. C., and R. A. Mintzer, Decreased bilayer stability due to transmembrane potentials, Phys. Lett., 86A, 57-59, Weaver, J. C., G.I. Harrison, J. G. Bliss, J. R. Mourant, and K. T. Powell, Electroporation: High frequency of occurrence of the transient high permeability state in red blood cells and intact yeast, FEBS Lett., 229, 30-34, Xie, T.-D., and T. Y. Tsong, Study of mechanisms of electric field-induced DNA transfection, II, Transfection by low amplitude, low frequency alternating electric fields, Biophys. J., 58, , Zeira, M., P.-F. Tosi, Y. Mouneimne, J. Lazarte, L. Sneed, D. J. Volsky, and C. Nicolau, Full-length CD4 electro-inserted in the erythrocyte membrane as a longlived inhibitor of infection by human immunodeficiency virus, PNAS, 88, , Zimmermann, U., P. Scheurich, G. Pilwat, and R. Benz, Cells with manipulated functions: New perspectives for cell biology, medicine and technology, Angew. Chem. Int. Educ. Eng., 20, , J. C. Weaver, Harvard-MIT Division of Health Sciences and Technology, Building 20A-128, 77 Massachusetts Avenue, Cambridge, MA (Received August 4, 1993; revised January 31, 1994; accepted January 31, 1994.)