Simulation of cell transmembrane potential

When the physics of pore size and resealing are not introduced, the dynamics of potential relaxation does not depend on the applied pulse duration, but rather on potential amplitude and RC parameters of the system. Therefore, for analysis of potential relaxation the 8 kV/cm × 1 μs pulse was used. The results of potential relaxation in different conductivity of extracellular medium are shown in Fig. 1.

Figure 1

FEM simulation of cell transmembrane voltage, where (A) – axisymmetric mesh structure; (B) – post-pulse cell transmembrane potential relaxation for different conductivity mediums. Electric field direction is shown to provide the information about the pulse polarity during application of PEF.

The cell was represented as an axisymmetric structure of material boundaries of different conductivity/thickness (Fig. 1A), which influenced the dynamics of cell depolarization (Refer to Fig. 1B). It can be seen in Fig. 1B that the higher was the conductivity of the extracellular medium the more effective the depolarization of the cell. Also, the polarization of the cell is altered when the conductivity of external medium is comparable or higher than the conductivity of the intracellular liquid, due to the changes of current densities.

The dynamics of cell polarization and depolarization during 200 ns and 100 μs pulses are shown in Fig. 2.

Figure 2

Dynamics of cell polarization and depolarization in extracellular mediums of different conductivity.

As it can be seen in Fig. 2, the lowest conductivity medium (0.05 S/m) due to RC charging nature of the cell limits the charging speed of the membrane. During 100 μs pulses the transient to reach the peak potential is in the range of 3.5 μs, which in comparison to duration of the pulse is not significant. However, the situation dramatically changes in the sub-microsecond range (200 ns), when the polarization time of the cell is a lot longer compared to the pulse duration. As a result, the induced transmembrane voltage during the same pulse (8 kV/cm × 200 ns) varies dramatically between mediums of different conductivity. Even a slight change (from 0.05 to 0.1 S/m) influences the increases of transmembrane voltage up to 55% due to differences in dynamics of polarization.

Experimental data

Electrotransfer in different conductivity mediums

The efficiency of electrotransfer for MC38/0 was evaluated in two buffers: STM – standard for in vitro electroporation experiments and HEPES – typical for in vitro calcium electroporation studies. Taken that the only difference was the buffer, the resultant conductivities were 0.1 S/m and 0.05 S/m, respectively. Parametric analysis of PEF influence on the uptake of YO-PRO-1 (YP) was performed. The results are summarized in Fig. 3. In order to establish that the changes in uptake between STM and HEPES were mainly influenced by the extracellular medium conductivity, from each range of parameters (Fig. 3A–D) a protocol was selected (EP1–EP4) to test the uptake when HEPES is mixed with highly conductive phosphate buffered saline (PBS) to a resultant conductivity of the final solution of 0.1 S/m (identical to STM based medium).

Figure 3

Dependence of YP uptake on applied PEF parameters and medium type in MC38 cell line, where (A) – conventional 100 μs × 8 protocols; (B) – 200 ns × 200 pulses protocols; (C) – 12 kV/cm × 8 pulses protocols; (D) – 60 kV/cm × 25 ns protocols; CTRL – untreated control; PBS – phosphate buffered saline.

As it can be seen in Fig. 3A, for the microsecond range (100 μs × 8), lower conductivity of the medium influenced higher permeabilization rate in the whole range of PEF amplitudes (0.6–1.5 kV/cm). Matching of the HEPES-based medium conductivity to STM resulted in lower permeabilization (compared to HEPES), however the difference was not statistically significant (P > 0.05).

Further, the 200 ns × 200 pulsing sequences were used in the 6–16 kV/cm range (Fig. 3B). The differences between HEPES and STM were more profound compared to the microsecond range protocols. However, the lower conductivity buffer (HEPES) resulted in lower permeabilization efficiency compared to the higher conductivity STM, which was also predicted by the FEM simulation (Refer to Fig. 2). Matching of the HEPES based solution conductivity to the STM resulted in identical response as in STM, which is in agreement with RC model of the cell.

The same methodology was applied to test the phenomena in 100–900 ns range and a fixed amplitude PEF was used (12 kV/cm). The results are summarized in Fig. 3C. It can be seen, that the tendency is consistent in the sub-microsecond range – lower conductivity medium negatively influences the permeabilization efficiency. Matching/increasing of the conductivity (HEPES+PBS) improves the efficiency of YP uptake.

Lastly, we performed the series of experiments in the nanosecond range (60 kV/cm × 25 ns), which were also consistent with the RC model of the cell (Fig. 3D). However, we were not able to observe a significant (P < 0.05) incremental effect in permeabilization with increase of the number of the pulses from 200 to 1200.

Susceptibilities of human cancer cell lines to electroporation

In order to establish that the observed effects of extracellular buffer conductivity are not cell specific, we have tested the selected protocols (EP1–EP4) on human skin melanoma (C32) and breast cancer (MCF7/DX) cell lines. The results are presented in Fig. 4.

Figure 4

Dependence of YP uptake with selected PEF protocols between different cell lines, where EP1–0.8 kV/cm × 100 μs × 8; EP2–8 kV/cm × 200 ns × 200; EP3–12 kV/cm × 500 ns × 8; EP4–60 kV/cm × 25 ns × 400.

As it can be seen in Fig. 4, different cells lines feature different susceptibility to electroporation, however, the tendency of the response in the context of extracellular medium conductivity is the same. In microsecond range (EP1), all three cell lines showed an increase in uptake of YP when a lower conductivity buffer was used (HEPES). Also, the skin amelanotic melanoma cell line was the most susceptible to the treatment followed by drug resistant breast cancer cells. The colon cancer (MC38/0) cell line was the least susceptible to PEF and the result was consistent in the whole range of parameters (EP1–EP4).

Metabolic activity of cells after calcium electroporation

In order to achieve high efficiency of calcium electroporation, high permeabilization rate of the cells must be ensured to maximize the electrotransfer. Therefore, for viability evaluation experiments (based on MTT assay) the energy of (EP1–EP4) was increased to ensure saturated permeabilization (EP5–EP8). Also, two concentrations of calcium were used (2 mM and 5 mM). All the experiments were performed in HEPES buffer. The 2 mM concentration was selected based on the available knowledge on calcium electroporation. It is known that a threshold in concentration exists when the calcium electrotransfer starts to be effective, while 2 mM is an optimal dose across many cell lines20. The resultant conductivity of the medium during the 2 mM Ca2+ electroporation procedure was 0.08 S/m. The 5 mM concentration (medium conductivity of 0.1 S/m) was selected to test if there is any treatment efficacy dependence on calcium concentration in the sub-microsecond range, which was not covered in literature previously. The results are summarized in Fig. 5.

Figure 5

Viability of different cell lines evaluated based on MTT assay after calcium electroporation, where EP5–1.2 kV/cm × 100 μs × 8; EP6–12 kV/cm × 200 ns × 200; EP7–12 kV/cm × 800 ns × 8; EP8–60 kV/cm × 25 ns × 1200.

As it can be seen in Fig. 5, the metabolic activity data are in agreement with permeabilization experiments in terms of different susceptibility of cells to pulsed electric field. The C32 line was the most susceptible to treatment, followed by MCF7/DX. The MC38/0 line showed the weakest response to the treatment. The differences in efficacy between calcium concentrations were statistically non-significant in absolute majority of experimental instances independently on the cell line, which implies that the efficacy of calcium electroporation is mostly dependent on the applied parameters of PEF/cell susceptibility and cannot be compensated by the increase of the calcium dose.

Taking into account the difference in electroporation efficacy between different conductivity buffers, we also expected to observe a reflection of the observed phenomena in the viability data. However, it was not the case. Independently on the applied protocol, the differences in metabolic activity in the context of extracellular medium conductivity were not statistically significant.

Aquaporin-4 and VDAC1/Porin immunostaining

The expression of two membrane proteins: aquaporin-4 (AQ-4), which forms a water-specific channel and VDAC1/Porin (a mitochondrial channel involved in cell volume regulation and apoptosis) were further analyzed in the study.

In case of melanoma (C32) the number of cells was reduced and the morphology was altered after electroporation and in particular with calcium ions (Table 1 and Fig. 6a). We have observed a significant decrease of cell volume due to cell shrinkage and loss of adhesion by filopodia. However, the levels of AQ-4 were the same as in the control samples without PEF treatment.

Table 1 Positive grading quantification of immunocytochemical staining of Aquaporin-4 expression in the three different cell lines: C32 – human amelanotic melanoma; MCF-7/DOX – human breast adenocarcinoma cells resistant to doxorubicin; MC38/0 – murine colon adenocarcinoma.
Figure 6

Immunoassayed reaction with anti-aquaporin-4 antibody detected in (a) amelanotic human melanoma cells (C32); (b) human resistant breast adenocarcinoma cells (MCF-7/DX) and (c) murine colon adenocarcinoma cell (MC38/0), where EP5–1.2 kV/cm × 100 μs × 8; EP6–12 kV/cm × 200 ns × 200; EP7–12 kV/cm × 800 ns × 8; EP8–60 kV/cm × 25 ns × 1200.

In case of breast adenocarcinoma cells (MCF-7/DX) a slight increase of AQ-4 immunoassayed reaction when exposed to calcium ions was observed. The combination with PEF treatment triggered an increase of AQ-4 expression, i.e. EP6 (97% positive cells with 2 mM Ca2+). At the same time, EP4 parameter caused a slight decrease of the immune reaction, however, cell number was significantly reduced. Colon cancer cells revealed relatively low expression of AQ-4 in control samples (23%), while both calcium ions and electroporation alone increased the immunostained reaction (61% and 78%, respectively). The combined protocols (PEF + CaCl2) enhanced the intensity of the reaction and the percentage of expressing cells for all protocols.

Various levels of expression of VDAC1-porin channel in C32, MCF-7/DX and MC38 cells were also investigated. Amelanotic melanoma and colon cancer cells showed the most intense reaction, whereas lower level of the reaction was exhibited in resistant breast cancer cells. The results of VDAC1 immunoassay are presented in Table 2 and Fig. 7. A significant increase of the immune reaction after calcium electroporation was observed (100% stained cells). The altered cell morphology, i.e. reduction of cell size due to shrinking and a reduced number of cells were detected (Fig. 7a). In case of breast cancer cells the increase of VDAC1 expression was detected for nanosecond protocols EP6, EP7, EP8, and when calcium electroporation was used (Fig. 7b). Similarly, colon cancer cells showed the highest increase of VDAC1 expression when CaEP was used (almost 100% of stained cells). Nanosecond range pulses provoked breaking up of the cells from grouped culture into smaller populations and cell shrinking (Fig. 7c).

Table 2 Positive grading quantification of immunocytochemical staining of VDAC1 expression in the three different cell lines: C32 – human amelanotic melanoma; MCF-7/DOX – human breast adenocarcinoma cells resistant to doxorubicin; MC38/0 – murine colon adenocarcinoma.
Figure 7

Immunoassayed reaction with anti-VDAC1 antibody detected in (a) amelanotic human melanoma cells (C32); (b) human resistant breast adenocarcinoma cells (MCF-7/DX) and (c) murine colon adenocarcinoma cell (MC38/0), where EP5–1.2 kV/cm × 100 μs × 8; EP6–12 kV/cm × 200 ns × 200; EP7–12 kV/cm × 800 ns × 8; EP8–60 kV/cm × 25 ns × 1200.

Source link