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Electroporation uses electric pulses to promote delivery of DNA and drugs into cells. This study presents a model of electroporation in a spherical cell exposed to an electric field. The model determines transmembrane potential, number of pores, and distribution of pore radii as functions of time and position on the cell surface. For a 1-ms, 40 kV/m pulse, electroporation consists of three stages: charging of the cell membrane (0-0.51 micros), creation of pores (0.51-1.43 micros), and evolution of pore radii (1.43 micros to 1 ms). This pulse creates approximately 341,000 pores, of which 97.8% are small ( approximately 1 nm radius) and 2.2% are large. The average radius of large pores is 22.8 +/- 18.7 nm, although some pores grow to 419 nm. The highest pore density occurs on the depolarized and hyperpolarized poles but the largest pores are on the border of the electroporated regions of the cell. Despite their much smaller number, large pores comprise 95.3% of the total pore area and contribute 66% to the increased cell conductance. For stronger pulses, pore area and cell conductance increase, but these increases are due to the creation of small pores; the number and size of large pores do not increase.

Electroporation, in which electric pulses create transient pores in the cell membrane, is becoming an important technique for gene therapy. To enable entry of supercoiled DNA into cells, the pores should have sufficiently large radii (>10 nm), remain open long enough for the DNA chain to enter the cell (milliseconds), and should not cause membrane rupture. This study presents a model that can predict such macropores. The distinctive features of this model are the coupling of individual pores through membrane tension and the electrical force on the pores, which is applicable to pores of any size. The model is used to explore the process of pore creation and evolution and to determine the number and size of pores as a function of the pulse magnitude and duration. Next, our electroporation model is combined with a heuristic model of DNA uptake and used to predict the dependence of DNA uptake on pulsing parameters. Finally, the model is used to examine the mechanism of a two-pulse protocol, which was proposed specifically for gene delivery. The comparison between experimental results and the model suggests that this model is well-suited for the investigation of electroporation-mediated DNA delivery.

This study expands a previously developed model of a single cell electroporated by an external electric field by explicitly accounting for the ionic composition of the electroporation current. The previous model with non-specific electroporation current predicts that both the transmembrane potential V(m) and the pore density N are symmetric about the equator, with the same values at either end of the cell. The new, ion-specific case predicts that V(m) is symmetric and almost identical to the profile from the non-specific case, but N has a profound asymmetry with the pore density at the hyperpolarized end of the cell twice the value at the depolarized end. These modeling results agree with the experimentally observed preferential uptake of marker molecules at the hyperpolarized end of the cell as reported in the literature. This study also investigates the changes in intracellular ionic concentrations induced around an electroporated single cell. For all ion species, the concentrations near the membrane vary significantly, which may explain the electrical disturbances observed experimentally after large electric shocks are delivered to excitable cells and tissues.

This study develops a model for a single cell electroporated by an external electric field and uses it to investigate the effects of shock strength and rest potential on the transmembrane potential V(m) and pore density N around the cell. As compared to the induced potential predicted by resistive-capacitive theory, the model of electroporation predicts a smaller magnitude of V(m) throughout the cell. Both V(m) and N are symmetric about the equator with the same value at both poles of the cell. Larger shocks do not increase the maximum magnitude of V(m) because more pores form to shunt the excess stimulus current across the membrane. In addition, the value of the rest potential does not affect V(m) around the cell because the electroporation current is several orders of magnitude larger than the ionic current that supports the rest potential. Once the field is removed, the shock-induced V(m) discharges within 2 micros, but the pores persist in the membrane for several seconds. Complete resealing to preshock conditions requires approximately 20 s. These results agree qualitatively and quantitatively with the experimental data reported by Kinosita and coworkers for unfertilized sea urchin eggs exposed to large electric fields.

The response of a cell to an external electric field is investigated using dimensional analysis and singular perturbation. The results demonstrate that the response of a cell is a two-stage process consisting of the initial polarization that proceeds with the cellular time constant (< 1 microseconds), and of the actual change of physiological state that proceeds with the membrane time constant (several milliseconds). The second stage is governed by an ordinary differential equation similar to that of a space-clamped membrane patch but formulated in terms of intracellular rather than transmembrane potential. Therefore, it is meaningful to analyze the physiological state and the dynamics of a cell as a whole instead of the physiological states and the dynamics of the underlying membrane patches. This theoretical result is illustrated with an example of an excitation of a cylindrical cell by a transverse electric field.