Modeling a Conventional Electroporation Pulse Train: Decreased Pore Number, Cumulative Calcium Transport and an Example of Electrosensitization.

Pulse trains are widely used in electroporation (EP) for both general biomedical research and clinical applications such as nonthermal tumor ablation. Here we use a computational method based on a meshed transport network to investigate a cell system model's response to a train of identical, evenly spaced electric field pulses. We obtain an unexpected result: the number of membrane pores decreases during the application of twenty 1.0 kV/cm, 100 µs pulses, delivered at 1 Hz. This pulse train initially creates 13,000 membrane pores, but pore number decreases by a factor of 15 to about 830 pores throughout subsequent pulses. We conclude that pore number can greatly diminish during a train of identical pulses, with direct consequences for the transport of solutes across an electroporated membrane. Although application of additional pulses is generally intended to increase the effects of EP, we show that these pulses do not significantly enhance calcium delivery into the cell. Instead, calcium delivery can be significantly increased by varying inter-pulse intervals. We show that inserting a 300-s interruption midway in a widely used eight-pulse train (a protocol for electrosensitization) yields a ∼ twofold delivery increase. Overall, our modeling shows support for electrosensitization, in which multiple pulse protocols that maximize pore number over time can yield significant increase of transport of calcium compared to standard pulse trains.

Basic features of a cell electroporation model: illustrative behavior for two very different pulses.

Science increasingly involves complex modeling. Here we describe a model for cell electroporation in which membrane properties are dynamically modified by poration. Spatial scales range from cell membrane thickness (5 nm) to a typical mammalian cell radius (10 µm), and can be used with idealized and experimental pulse waveforms. The model consists of traditional passive components and additional active components representing nonequilibrium processes. Model responses include measurable quantities: transmembrane voltage, membrane electrical conductance, and solute transport rates and amounts for the representative "long" and "short" pulses. The long pulse--1.5 kV/cm, 100 µs--evolves two pore subpopulations with a valley at ~5 nm, which separates the subpopulations that have peaks at ~1.5 and ~12 nm radius. Such pulses are widely used in biological research, biotechnology, and medicine, including cancer therapy by drug delivery and nonthermal physical tumor ablation by causing necrosis. The short pulse--40 kV/cm, 10 ns--creates 80-fold more pores, all small (<3 nm; ~1 nm peak). These nanosecond pulses ablate tumors by apoptosis. We demonstrate the model's responses by illustrative electrical and poration behavior, and transport of calcein and propidium. We then identify extensions for expanding modeling capability. Structure-function results from MD can allow extrapolations that bring response specificity to cell membranes based on their lipid composition. After a pulse, changes in pore energy landscape can be included over seconds to minutes, by mechanisms such as cell swelling and pulse-induced chemical reactions that slowly alter pore behavior.

Emergence of a large pore subpopulation during electroporating pulses.

Electroporation increases ionic and molecular transport through cell membranes by creating transient aqueous pores. These pores cannot be directly observed experimentally, but cell system modeling with dynamic electroporation predicts pore populations that produce cellular responses consistent with experiments. We show a cell system model's response that illustrates the life cycle of a pore population in response to a widely used 1 kV/cm, 100 µs trapezoidal pulse. Rapid pore creation occurs early in the pulse, followed by the gradual emergence of a subpopulation of large pores reaching ~30 nm radius. After the pulse, pores rapidly contract to form a single thermally broadened distribution of small pores (~1 nm radius) that slowly decays. We also show the response of the same model to pulses of 100 ns to 1 ms duration, each with an applied field strength adjusted such that a total of 10,000±100 pores are created. As pulse duration is increased, the pore size distributions vary dramatically and a distinct subpopulation of large pores emerges for pulses of microsecond and longer duration. This subpopulation of transient large pores is relevant to understanding rapid transport of macromolecules into and out of cells during a pulse.

A brief overview of electroporation pulse strength-duration space: a region where additional intracellular effects are expected.

Electroporation (EP) of outer cell membranes is widely used in research, biotechnology and medicine. Now intracellular effects by organelle EP are of growing interest, mainly due to nanosecond pulsed electric fields (nsPEF). For perspective, here we provide an approximate overview of EP pulse strength-duration space. This overview locates approximately some known effects and applications in strength-duration space, and includes a region where additional intracellular EP effects are expected. A feature of intracellular EP is direct, electrical redistribution of endogenous biochemicals among cellular compartments. For example, intracellular EP may initiate a multistep process for apoptosis. In this hypothesis, initial EP pulses release calcium from the endoplasmic reticulum, followed by calcium redistribution within the cytoplasm. With further EP pulses calcium penetrates mitochondrial membranes and causes changes that trigger release of cytochrome c and other death molecules. Apoptosis may therefore occur even in the presence of apoptotic inhibitors, using pulses that are smaller, but longer, than nsPEF.