Scaling relationship and optimization of double-pulse electroporation

Abstract

The efficacy of electroporation is known to vary significantly across a wide variety of biological research and clinical applications, but as of this writing, a generalized approach to simultaneously improve efficiency and maintain viability has not been available in the literature. To address that discrepancy, we here outline an approach that is based on the mapping of the scaling relationships among electroporation-mediated molecular delivery, cellular viability, and electric pulse parameters. The delivery of Fluorescein-Dextran into 3T3 mouse fibroblast cells was used as a model system. The pulse was rationally split into two sequential phases: a first precursor for permeabilization, followed by a second one for molecular delivery. Extensive data in the parameter space of the second pulse strength and duration were collected and analyzed with flow cytometry. The fluorescence intensity correlated linearly with the second pulse duration, confirming the dominant role of electrophoresis in delivery. The delivery efficiency exhibited a characteristic sigmoidal dependence on the field strength. An examination of short-term cell death using 7-Aminoactinomycin D demonstrated a convincing linear correlation with respect to the electrical energy. Based on these scaling relationships, an optimal field strength becomes identifiable. A model study was also performed, and the results were compared with the experimental data to elucidate underlying mechanisms. The comparison reveals the existence of a critical transmembrane potential above which delivery with the second pulse becomes effective. Together, these efforts establish a general route to enhance the functionality of electroporation.

Figure 1

An exemplary double pulse used in the delivery of Fluorescein-Dextran into 3T3 mouse fibroblasts. The first pulse was 100,000 V/m in strength and 0.001 s in duration. The second pulse was 30,000 V/m in strength and 0.01 s in duration. The signal was measured using the software LABVIEW (National Instruments, Austin, TX). To see this figure in color, go online.

Figure 2

Exemplary cell analysis with dot plots. (a) Control cells that were not pulsed. These cells are plotted with respect to forward-scatter (abscissa) and side-scatter (ordinate). The cell population in panel a is separated from debris using a circular gate. (b–d) Abscissa represents the fluorescence signal due to the uptake of Fluorescein-Dextran (FD); the ordinate, 7-Aminoactinomycin D (7-AAD). (Solid lines) Separation of the regions of uptake and no-uptake of the respective dyes. Cells in panel b are the gated cells from panel a, which were not pulsed. Cells in panel c received a single pulse of E₁ = 100,000 V/m and t₁ = 0.001 s. Cells in panel d received an additional pulse of E₂ = 30,000 V/m and t₂ = 0.1 s with no delay with respect to the first pulse. To see this figure in color, go online.

Figure 3

Fluorescein-Dextran fluorescence signal for three different second-pulse field strengths at different second-pulse durations. (a) E₂ = 25,000 V/m; (b) E₂ = 50,000 V/m; (c) E₂ = 100,000 V/m. The cell populations of each distribution are obtained from the Q3 quadrant in Fig. 2, b–d.To see this figure in color, go online.

Figure 4

(a and b) The normalized fluorescence (NF) of intracellular Fluorescein-Dextran as a result of double-pulse electroporation. (Symbols) Experimental data; (curves) least-square fitting. For all cases, the first pulse was always E₁ = 100,000 V/m and t₁ = 0.001s. To see this figure in color, go online.

Figure 5

The delivery rate per unit time (α, circles) as a function of E₂. The value α is extracted from Fig. 4a by calculating the slopes of the linearly fitted lines (Eq. 10), and the error bars represent the 95% confidence interval of the fitting. The correlation between α and E₂ can be further approximated by a least-square sigmoidal fitting (dashed). The coefficient of determination is R² = 0.97.

Figure 6

The percentage of viable cells after double-pulse electroporation. (Symbols) Experimental data; (curves) least-square fitting. For all cases, the first pulse was always E₁ = 100,000 V/m and t₁ = 0.001 s. To see this figure in color, go online.

Figure 7

Scaling law of viability with respect to the electrical energy (E₂²t₂). (Symbols) Experimental data; (dashed curve) least-square fitting given by Eq. 12. Viability decreases linearly with increasing electrical energy. To see this figure in color, go online.

Figure 8

(a) Polar distribution of the pore area density (PAD). For this case, E₂ = 30,000 V/m, t₂ = 0.001 s, θ = 0 for the cathode-facing pole, from which side most of the negatively charged FD molecules enter. (b) The evolution of TPA as a function of time. For all cases, t₂ = 0.001 s. To see this figure in color, go online.

Figure 9

(a) Simulated results of delivery of total FD (TFD) and (b) delivery rate of Dextran (α_sim) plotted as a function of t₂ and E₂. To see this figure in color, go online.

Figure 10

NF as a function of E₂ and S (Eq. 15). (a) The curves can be regarded as constant-viability contours in the phase space of E₂ and NF. A maximum value of NF is reached at E₂ = 58,000 V/m for all S values. (b) The maximum value of NF for each value of S in panel a. An inverse linear correlation is observed. To see this figure in color, go online.