# Efficient Gene Transfection by Electroporation--In Vitro and In Silico Study of Pulse Parameters
## 3 Results
### Modeling the Probability of pDNA and Cell Membrane Contact during GET
#### 3.6.2 HF-BP Pulses
Figure 14: HF-BP pulses: Evolution of \(P(X,t)\) and the corresponding Probability of Successful Contact \(PSC(t)=1-\int_{-B_{L}}^{+B_{R}}P(X,t)dX\) for \(B_{L},B_{R}=134\) nm (corresponding to 500 \(\mathrm{\SIUnitSymbolMicro g}\)/mL) during a sequence of 32 bipolar pulses (1 burst) at an electric field intensity of 1.25 kV/cm (Table 1 for C2C12 cells). (**A–E**) represent cases without free energy barrier and (**F–J**) represent cases with free energy barrier. The dashed lines in (**E,J**) represent the time at which the sequence of 32 pulses (i.e., 1 burst) ends. The difference between the cases without and with the free energy barrier can be seen in the evolution of \(P(X,t)\) after the burst (comparing Figure 14D with Figure 14I). Similar to ns pulses, it is less probable for the pDNA molecule to come in contact with the cell membrane by diffusion only in the presence of the free energy barrier. As a result, there is higher probability for the pDNA molecule to stay within the domain \(X\in[-B_{L},\,B_{R}]\). Correspondingly, \(PSC(t)\) begins to rise at a much later time in the presence of the free energy barrier (Figure 14J) compared to the case without the free energy barrier (Figure 14E). \(PSC(t)\) also reaches a lower final value of only silightly greater than 0.3 at the end of the burst. \(PSC(t)\) is evaluated using \((B_{L},B_{R})\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 \(\mu\)g/mL to 15 \(\mu\)g/mL, respectively, and is shown in Figure 15A for the case without the free energy barrier and in Figure 15B for the case with the free energy barrier. For all ranges of \((B_{L},B_{R})\) tested, \(PSC(t)\) rises post-burst termination (32 bipolar pulses) through the diffusive process. As seen from Figure 15A, and similar to nanosecond pulses, \(PSC(t)\) starts to rise from \(t\sim\) 0.2 ms for the lowest \((B_{L},B_{R})\) = 77 nm. Furthermore, the time at which \(PSC(t)\) begins to rise depends on \((B_{L},B_{R})\), and \(PSC(t)\) starts to rise earlier for lower \((B_{L},B_{R})\). A similar trend was observed for the case with the free energy barrier; however, the rise in \(PSC(t)\) was delayed (to \(t\sim\) 10 ms for the lowest \((B_{L},B_{R})\) = 77 nm) and \(PSC(t)\) attains a lower final value (at = 1 s) compared to the case without the free energy barrier. The evolution of \(PSC(t)\) is similar for nanosecond and HF-BP pulses. Figure 16 shows \(PSC(t)\) using \(B_{L},B_{R}\) = 134 nm (500 \(\mu\)g/mL) for a 200 ns pulse, a 500 ns pulse, and a bipolar burst. Irrespective of the pulse duration (200 ns, 500 ns, or a burst of 2 \(\mu\)s bipolar pulses), \(PSC(t)\) starts to rise post-pulse/burst termination from around \(t\sim\) 1 ms (for the case without the free energy barrier Figure 16A) and \(t\sim\) 20 ms (for the case with the free energy barrier Figure 16B) and rises at the same rate. This indicates that the electrophoresis provided by these nanosecond and HF-BP pulses is insufficient to establish a pDNA contact with the cell membrane, and \(PSC(t)\) rises due to diffusion. The solid vertical line in Figure 16A,B represents the onset of the next 200 ns or 500 ns pulse (pulse re  
Figure 15: Evolution of \(PSC(t)\) for different \((B_{L},B_{R})\) ranging from 77 nm to 433 nm, corresponding to concentrations ranging from 2500 \(\mu\)g/mL to 15 \(\mu\)g/mL, respectively, for a sequence of 32 bipolar pulses (1 burst) at an electric field intensity of 1.25 kV/cm (Table 1 for C2C12 cells): (**A**) without free energy barrier and (**B**) with free energy barrier. Dashed lines represent the time at which the sequence of 32 pulses (i.e., 1 burst) ends. It is worthwhile to note that for ns pulses, a single pulse was considered, whereas for HF-BP pulses, 32 bipolar pulses (or 1 burst) were considered.