Electric Field Induced Changes in Membrane Properties

Changes in transmembrane potential and membrane conductance accompany many instances of membrane-field interaction. These events include both useful and harmful effects of an electric field on biological systems. Examples of such phenomena include electroporation, nerve conduction and high-voltage injury.

Electroporation: An important application of strong electric fields on cells is in membrane electroporation. Electroporation of cells uses intense electric pulses to alter membrane permeability for increased uptake of drugs, molecular probes, and DNA. Electroporation has many applications in medicine and biology, such as introduction of DNA into living cells, fusion of cells, insertion of proteins into cell membranes, improving drug delivery and its effectiveness in chemotherapy of cancerous cells, and alteration of genetic expression in living cells (Tsong, 1991; Neumann et al. 1989; Chang et al. 1992; Blank, 1993; Weaver, 1993; Orlowski and Mir, 1993). Electroporation and its related phenomena such as electrofusion and bleb formation reflect the basic bioelectrochemistry of cell membranes and are thus important in the study of membrane structure and function.

The underlying mechanism of electroporation involves increasing membrane permeability using a strong electric field. Under normal physiological conditions, a bilayer lipid membrane made of lipid extracts of cells is a good barrier for ions and hydrophilic molecules. The membrane conductance to is typically or smaller (Tien, 1974). This permeation barrier is readily modified by imposing a transmembrane potential. When an intense transmembrane electric field exceeding the dielectric strength of a cell membrane is applied, the membrane specific conductance increases dramatically and can reach as high as in microseconds (Hibino et al. 1993). Cell membranes can sustain as much as 1 V of transmembrane potential, i.e., an electric field strength of 2,000 kV/cm, when microsecond to millisecond electric pulses are used (Coster et al. 1975).

The proposed model can be used to determine pore distribution and membrane conductance for pulses used in electroporation. These parameters will be useful in selecting pulse parameters in electroporation applications based on the desired size of pores. The strong field applied during electroporation causes local heating which could also be estimated using the predictions of the proposed model.

High-voltage Electric Shock: High-voltage electrical shock is another event in which a strong electric field leads to membrane poration and consequent changes in membrane electrical properties. Such intense fields elevate the transmembrane potential by hundreds of mV thus decreasing the energy barrier allowing the creation of large radii pores. Knowledge of electropore population is necessary for the design of a therapeutic treatment for electrical trauma.

High-voltage electrical trauma frequently leads to selective, yet, extensive destruction of muscle and nerve tissue (Lee, 1991). Many of the immediate clinical signs of a major electrical injury relate to neuromuscular damage revealed by intense muscular spasm. These observations suggest that muscle cell membrane rupture is one of the primary mechanisms of tissue damage in high-voltage shock. Theoretical and experimental evidence suggests that long skeletal muscle and nerve cells are vulnerable to plasma membrane rupture by electrical breakdown (Gaylor et al. 1988). This breakdown occurs as a result of the formation of pores on cell membrane leading to an increased membrane conductivity and diffusive permeability and to changes in the spatial distribution of transmembrane potential. Therefore, the change in transmembrane potential distribution is a measure of the physiologic state of a cell following an electric shock. Investigation of changes in membrane properties introduced by an electric field is crucial for understanding the consequences of high-voltage electric shock and in designing an effective treatment for these injuries.

One method of treating electrical injury is by inducing the sealing of membrane pores. Nonionic block copolymer surfactants have been shown to seal electropermeabilized skeletal muscle cells (Lee et al. 1992). These surfactants form a family of non-toxic, non-ionic surface-active agents containing a hydrophobic propylene oxide chain sandwiched between two sequences of hydrophilic ethylene oxide chains. The properties of these surfactants are dependent on the ratio of the length of the hydrophobic chain to that of the hydrophilic chain. The choice of surfactants for sealing of membrane pores depends on the size and population of such pores. Extension of the proposed model to breakdown potentials will be useful in designing optimal surfactants for treating electrical injury.

The proposed non-uniform cable model will be designed to study electropore distribution in terms of electrical properties of the cell membrane. Changes in these properties dictate the kinetics of pore formation and evolution. The linear cable model will be used in the proposed work to represent the electrical properties of a skeletal cell membrane.

Linear Cable Theory of Electrophysiologic Behavior

Membrane pores arising from the application of an external electric field in such events as electroporation and high-voltage electric injury contribute to changes in the electrical properties of the cell membrane. The objective of this project is to estimate these changes in membrane electrical properties and to determine the distribution of membrane pores.

Existing models depict a cell membrane as having spatially uniform electrical properties (Jack et al. 1975). According to these models, the cell membrane acts as an insulating shell in a continuous conductor causing the voltage across the cell diameter to appear mainly across the relatively thin membrane. This results in a field amplification of a few orders of magnitude. This field amplification at the cell membrane level is a trigger for the initiation of many cell biological effects. Therefore, it is critical to be able to determine the perturbations to the transmembrane potential induced by exposure to an electric field if a full understanding of the ensuing cellular responses is to be reached.

Conduction of the cell membrane has been studied extensively with the standard cable model where a cylindrical fiber is considered to behave like a co-axial cable with leakage between the intracellular and extracellular media (Rall, 1977; Joyner et al. 1983; Katz, 1966). In a cable model, electrical properties of the plasma membrane are represented by a series of parallel resistors and capacitors. This lumped parameter circuit model of the membrane is combined with the resistances of the intracellular and extracellular media to analyze the effects of an external field. The cable equations that represent the cable circuit are solved to determine the spatial distribution of induced transmembrane potential (Ranck, 1963; Sten-Knudsen, 1960).

The cable circuit model forms the basis for representing transmembrane potential distribution in the proposed model with a modification that the cell membrane is assumed to be spatially non-uniform. The non-uniformity results from the presence of membrane pores which is modeled by the membrane pore theory.

Membrane Pore Theory

Lack of a rigorous experimental method to measure membrane pore dynamics has prompted the development of several models to study the formation of membrane pores in the context of electroporation (Abidor et al. 1979; Sugar and Neumann, 1984; Weaver and Mintzer, 1986; Saulis and Venslauskas, 1993). Although the mechanism by which electroporation occurs is not completely understood, it is generally believed that a rapid structural rearrangement of membrane occurs, whereby many aqueous pathways ("pores") perforate the membrane (Freeman et al. 1994).

Early attempts to use the presence of local defects (pores) to explain increased membrane permeabilization were made by Abidor et al. (1979) . Sugar and Neumann (1984) treated electroporation as a stochastic process and modeled the aqueous pores as periodic block structures. Independently, Weaver and Mintzer (1986) developed a model based on the hypothesis that a large number of transient aqueous pores continually present on the bilayer membrane expand, leading to increased conduction. This model was extended to study pore density and molecular transport under charge-injection conditions (Barnett and Weaver, 1991; Freeman et al. 1994). Recently, (Saulis and Venslauskas 1993) developed a model assuming that the creation and disappearance of metastable pores are random one-step processes.

The aqueous pore theory (Weaver and Mintzer, 1986) has been refined to estimate pore distribution and molecular transport across bilayer lipid membranes (Barnett and Weaver, 1991; Freeman et al. 1994). This model will be used in the proposed work as the basis to represent the creation and evolution of membrane pores. According to the membrane pore theory, transient pores appear on the membrane as thermal defects. These pores are assumed to spontaneously contract in the absence of expansive forces. Random bombardment of water molecules generates a fluctuating macroscopic pressure, leading to a distribution of pore radii. An applied field contributes to this force leading to the expansion of the existing pores to larger radii. The distribution of pores is thus described as a balance between the restoring force and the field induced expanding force (Barnett and Weaver, 1991).

The frameworks of aqueous pore theory and cable theory are used in this project to model the changes in the electrical properties of a skeletal muscle cell in the presence of an external field. These changes are coupled to the pore energy to determine the population of membrane pores.

Experimental Techniques For Electroporation Studies

The kinetics of electroporation involve initial molecular reorganization of the cell membrane and its secondary effect, pore formation, processes that occur in nanoseconds to subsecond time scales (Tsong, 1991). This investigation was motivated by the lack of experimental techniques capable of measuring the kinetics of membrane property changes with adequate temporal resolution.

Experimental techniques used to study electroporation on skeletal muscle cell membranes include morphological investigation using an electron microscope with freeze fracture (Chang and Reese, 1990) and permeability studies employing a fluorescent dye (Lee et al. 1992). Tsong and colleagues (1991) measured the conductivity of an erythrocyte suspension to compare membrane electroporation and field-induced effects on ATPase (Teissie and Tsong, 1980; Serpersu and Tsong, 1983). These methods involve measurements taken after the electrical shock had occurred and have a time resolution of 0.1 sec or greater.

An alternate method permitting higher time resolution employs fast potentiometric dyes to monitor transmembrane potential change. Hibino et al. (1991) used a submicrosecond imaging system to study electroporation in a sea urchin egg. The charge injection/relaxation method has also been used in measuring nanoampere magnitude transmembrane currents at high time resolution (Benz and Zimmerman, 1980, 1981; Chernomordik et al. 1983). These methods are useful only for the measurement of events occurring immediately after an electric shock and not those occurring during the pulse.

Measurements of transmembrane current and potential in this project will employ a voltage clamp technique. This method provides the capability to measure transmembrane current during a constant transmembrane potential pulse. The voltage clamp methodology has been used to study electroporation primarily in artificial lipid bilayer preparations (Abidor et al. 1979; Chernomordik et al. 1987; Glaser et al. 1988) and sparingly in live cells (O'Neill and Tung, 1991). This investigation will use an improved double vaseline gap voltage clamp (Chen and Lee, 1994) to measure transmembrane current and potential changes.